There is some useful stuff in here about when you and your child have clashing sensory needs - which I think the "unable to escape" feeling probably is that.
There are also things which might feel a bit dismissive but could help you cope such as turning on loud music in the car. And in terms of noise blocking, passive noise cancellation (ie, blocking your ears somehow) is more effective against higher pitches which change suddenly, like a child's voice, whereas ANC is more effective against lower, more consistent pitches like aeroplane/traffic/fan noise. So actually some proper ear defenders or the 3M earplugs as someone else suggested can be more effective. I do not like wearing either of these myself as I don't like the physical sensation, but they can be a sort of "least worst" in some situations.
If you feel that you are not safe to drive with less hearing ability, then consider that DD's screaming in itself is also likely to be blocking your ability to hear things. So if you feel that adding hearing protection or loud music to the entire effect would be dangerous, it might actually be worth treating this kind of incident as an emergency and pulling over as soon as it is safe to do so and see if you can wait for the "loop" to end before you start to drive again. TBH I personally cannot drive - I never managed to pass a driving test - so I don't have a huge amount of experience with driving and I don't know whether it's safe or not, but as you do drive I think you could probably make a judgement here. Certainly if you're getting to the point of screaming, I'd wonder if it's even possible to be focused on the road at that point so it might be best, even if inconvenient, to stop (though I could be totally wrong!!)
The thing with the specific pitch of a human scream, a child's whine, a baby's cry, is that these all occupy a part of the sound spectrum which is not used by anything else and therefore you are hard wired by evolution to respond to it as an emergency. In fact, we use the same frequency to create the sound used in things like fire alarms and sirens, specifically because it triggers escalation in the sympathetic nervous system which kicks us into a more alert mode where we can act quickly and decisively, but it has the side effect that this more awake/alert/ready for action mode pushes us more into actions triggered by the amygdala, which is the brain area which deals with emotions, memories, learnt/automatic behaviour, and perception of danger. So when we are in more of an alert, ready to react state, we are also in more of a heightened emotional state.
I noticed that although you say it is more the physical/sensory - you do keep returning to variations on "I can't get her out of the loop/I can't get her to stop" which is why I asked the question. What I tend to find is that when my nerves are jangled by unpleasant sensory input, probably because I've gone into that more emotional centre, anything emotional is really heightened and I definitely do on some level feel that if my child is unhappy, it is an emergency and I need to solve their feeling. There is a popular line on social media currently that this is about your own feelings not being met as a child and I also don't especially relate to that, I think it's probably overly simplistic although it does obviously hit a note for a lot of people.
So on one level it can help to (generally, ie outside of the moment) do some reframing about DD being upset or wanting something (esp something impossible) does not mean that you need to provide it instantly, that it is OK for her to feel frustrated, impatient, upset, powerless, even distraught - at times - because in fact feelings themselves are not dangerous or harmful, they are not much fun, but they do pass. I think we do sometimes worry/get the message that children can be harmed or traumatised by experiencing hard feelings and I don't think this is true. I don't think feelings are completely unimportant, but I do think I was probably giving them more importance than was ultimately helpful. Some useful things I've found for reframing my own role in DC's emotions which don't totally invalidate/dismiss them, are Janet Lansbury's blog/podcast (more so than her books) and the book When Your Kids Push Your Buttons by Bonnie Harris. I've also recently been reading about the SPACE parenting approach which has some of the same themes, about not always feeling you have to rescue DC from difficult emotions and trusting them to be able to handle this themselves as well, and how to know when to do this vs when to hold back.
I did mention about ND before and this is because you keep saying that the issue is about you rather than DD, and I think you're right - whether or not DD is ND is essentially irrelevant, because it is highly unlikely that anything would be diagnosed at this age, and even if it was it's not going to instantly make the difficult behaviour stop, so you need a way to cope with it short term even if you can work on things for her such as managing overstimulation to try to reduce the incidence. The only useful thing about information that your DD might be ND is to confirm that this behaviour is unusually intense (which I think it could be, ND or not) and that most parents are not dealing with it to this extent - perhaps most children would wear themselves out within about 5-10 mins or be amenable to some of the distraction/redirection techniques. My youngest would - but TBH, I don't know what is typical any more.
But if you yourself might be ND, it could also be that your brain is actually responding to the same stimulus that other parents experience in a different way. It might be for example that other parents are more able to mentally "filter" out this kind of input. It might be that their emotional response comes on more gradually, giving them more time to notice and down-regulate. If you feel that you are coping with it until you are suddenly not, it might be worth trying to pay attention to things like sensations in your body that start up when you feel you might be getting towards the explosion point. As well as the physical sensory tools such as hearing protection, what can also help here IME is understanding that when your body goes into a more stressed/emotional state, talking yourself out of it with words is unlikely to help. What helps tends to be more physical, so either mimicking the body language of a calmer body state - consciously slowing your breathing, lowering your shoulders, making your movements slow and deliberate, keeping your own voice at a lower pitch and volume and adopting a more soothing tone, one tip I heard was to actually speak using the rhythm of a heartbeat (ba-DUM, ba-DUM) though this doesn't help me - the other things do. Then other ideas are anything which connects you back to your body and helps you feel "in the room" such as mindfulness where you focus on physical sensations e.g. your bum on the chair, your feet on the ground/pedals, your clothing, maybe open the window to feel the cold air, also EFT tapping, or visualisation e.g. of roots tying you firmly into the ground can feed into this kind of grounding/mindfulness technique. If not driving then something physical like stretches, dancing/jumping/shaking the stress off. Breathing techniques - box breathing, timed breathing etc. And the last one is to try to shift your brain out of danger mode and back into thinking/cognitive mode, by focusing on something which needs cognitive functions like mapping out the journey ahead of you, running through times tables or other maths, narrating the process of whatever you're doing, reciting poetry or a favourite book, singing along to a song or a very repetitive nursery rhyme like One Man Went to Mow, counting items of different colours, looking for things which start with different alphabet letters, putting on a podcast which is a quiz or having some kind of puzzle on the go you can access throughout the day, anything similar to any of this. Doing any of these out loud can be easier than trying to hold onto the information mentally, but again it's just to shift your focus.
Some useful resources I've found for offering me strategies when I feel like I'm edging towards losing control are Conscious Discipline, which talks a lot about the different brain states, and TheOTButterfly has a lot of info about sensory self-regulation strategies - she has a book coming out which might be good. And Emily/Amelia Nagoski have a book called Burnout which talks about "closing the stress cycle" although TBH I found their podcast interviews about the concept in the book much more useful than the book itself.
And also again - sometimes it's helpful simply to create space between the two of you, if it's safe and appropriate to do that. Either until she calms down, or just to give you the space to collect yourself/try to use one or more of these ideas so that you can re-emerge with a calmer approach. If you need to cry, or scream into a pillow or whatever while you have space that's fine. Leaving her alone might not feel like ideal parenting, but it is better than losing it and shouting. Ideally you're aiming to get to a point where you can be using the self-calming techniques much earlier in the process before you are close to shouting, but for me I had to start by using them at the end, before I could even recognise the earlier signs. And whether it's relevant for you or not - but I found that I often enter this kind of state when I have accidentally neglected to eat/drink/use the toilet/give myself breaks generally. So trying to do all of these things proactively so that I do not find myself in a place where I desperately need something also helps.
This is quite a lot of information in one post, so I would say copy and paste it somewhere, and divide it into things to explore outside of the moment and things to try in the moment, and for the things to try in the moment, either have this as a bullet pointed list you can access quickly on a phone, print it out and stick it on the fridge or in the bathroom, or just pick one idea to try (and know that it's unlikely you'll remember it every time) and see if it helps.
Lastly I know you said you didn't find your GP very helpful, but if you are really struggling to manage your own emotions, GPs can prescribe SSRIs which some people find helpful, and can be a temporary measure. You can also often self-refer to CBT which can also help you develop some tools to cope with difficult emotions in the moment. You could also look to see whether you have a Family Hub nearby as they are meant to be opening all over the country and in theory should be able to help support with things like this.