There's a fantastic book I absolutely love and found invaluable when my first was this age called When Your Kids Push Your Buttons. I think it's only 99p on Kindle.
I used to say it's like therapy in a book. It's obviously not as good as real therapy and if you've had serious childhood trauma then maybe that would be worth looking into, and I'd go paid rather than NHS if it's an option at all, but the book might be helpful as an interim measure. It helps you reframe your child's behaviour and examine your own reactions to it which helps you feel less attacked/personally victimised and that translates to more access to your rational brain in the moments when they are pushing every button.
I agree with the posts saying you sound burnt out and dysregulated yourself. When you have a child who is much more intense and needs much more co-regulation than average this is an absolute essential. When do you get a break? When was the last time you stayed overnight somewhere without the DC? Had a night out? Had a full day to yourself to use as you like? Do you have a space at home which is JUST yours (or at the very least, just for you and DH?)
Do you have ways to self-regulate when you're starting to boil over - do you know how to recognise that you are even starting to boil over? I don't have childhood trauma, but I do have ADHD and this was a huge thing for me because I felt like the "rage" would come on out of nowhere and actually I was simply unaware of the earlier signs that things were building up too much. Still working on the ways to self-regulate. My default is to disengage and that is not always appropriate or helpful.
If you have a reactive nervous system whether that's from trauma history or from some kind of ND then it's really difficult to parent a very intense child who needs a lot of co-regulation. It's such a cliche but you can't pour from an empty cup - you need to be able to regulate yourself before you can help them. Some of those ear plug things which filter out or dampen certain frequencies of sound might help if crying is triggering a "fight or flight" response in you. Not because you should ignore the crying but because it will help you react compassionately if your head isn't totally scrambled by the sound of it.
For a practical approach which might help your DD in the short term, I would look at either or both of: The book How To Talk So Kids Will Listen and Listen So Kids Will Talk, and then get the app (which is by Mythic Owl and costs about £4) so that when you find yourself in the middle of a tough moment you can open the app and be reminded quickly of the ideas you've read in the book, which often make sense when you read them, but then in the moment they leave your head entirely.
And/or look at The ABCs of Everyday Parenting course on Coursera, which helps you replace automatic responses like shouting, threatening, punishing with more effective ways to change behaviour and encourage replacement behaviours. It's designed really well, it's free and the videos are only about 10 mins long and you can watch half of one at a time if you like and I found it helpful from the first one.
AIBU can be extremely robust for parenting advice! So well done for sticking with the thread and don't pay too much heed to posters who just want to kick you when you're down without offering any actual advice. She is little and I think you can turn this around - you are not your parents, you are already doing better than they did, and you don't need to be perfect - it's about finding reliable things to replace your automatic responses, making time and space for your own needs so you're not running on empty, seeing her as a little person having a hard time rather than out to get you/give you a hard time, and apologising/repair when you mess up. Simple, not necessarily easy 
but very very worth it and IMO you can do this step by step.