I also had a situation like this for the first few months.
I’m not sure how much was hormonal/anxiety but I found it so hard to sleep in that first ‘shift’ when my husband was with the baby.
The baby also woke loads in that period which made it harder to sleep.
A few things:
I think we were both way too stressed about me sleeping which didn’t help. You can’t control his reaction, but tell him the pressure needs to be taken off, and if he stresses about it, ignore him. Sleep is not within your conscious control.
You’re not alone. You should definitely aim for 6 hours (even if broken) but remember that loads of people really struggle to get back to sleep after settling a baby, or to nap in the daytime. I was gobsmacked the amount of my friends that said the same thing. Whilst I was berating myself for being so weird and anxious and not being able to sleep (berating yourself doesn’t help!)
It will pass. You’ll be able to sleep more easily again. The baby will sleep and get back to sleep better, which helps, but also your anxiety about this will pass.
Banging your head is concerning, I would look around for free or low cost therapists from charities etc. Or pay if money is not the issue. I get that therapy doesn’t fix everything, and certainly doesn’t cure a tendency towards insomnia overnight. But you are clearly feeling emotional pain around the tiredness, perhaps understandably this engenders feelings of hopelessness, and a good therapist would help with the emotions surrounding this.
As past posters have said, 2hrs per night etc is not enough. But everyone has those nights sometimes, try and aim for more sleep without beating yourself up.
Weirdly I started sleeping better when I started doing all night wakings because husband was sick. It took the pressure off and I went straight back to sleep even if the baby woke very frequently. I wouldn’t necessarily recommend this as I did benefit from longer stretches of the ‘shift’ system, but worth considering how your mindset would change if that was the case (without actually doing the whole night yourself).
A couple of nights where he does the whole night or at least till 4 or 5am (either in a row or maybe once a week?) will really help you to reset, it did for me.
Also agree with pp - use formula for the night. I also expressed and again this contributed to the anxiety around sleep as I had to pump just to get any sleep.
Another vote for meditation as very important useful. Do this when you’re awake, and or other things you like for example reading or podcasts to take your mind off pressure to sleep.
I do remember this experience as very painful and stressful so you have my complete sympathy. I’m also a bad sleeper as a general rule pre baby.
If you did need or want to go on medication then you might need to stop breastfeeding and that is ok. Your mental and physical health is much more important. Although agree there should absolutely be more research into and awareness of medications that are safe when breastfeeding.
All the best from me