You poor thing, i really feel for you.
I was in a similar situation years ago. I was becoming unwell, was delirious from lack of sleep and felt myself slipping into depression.
I switched to formula at night and it was life changing for both me and my baby.
I did this against the very strong advice of the public health nurse who said that baby would experience nipple confusion and would reject the breast (didn't happen but even if it did....?).
Her advice was to persevere as things would get better, that the first six weeks are the hardest etc.
I was sitting in front of her crying at the time, not having slept for three nights and thinking that i did not want to continue living. So zero respect here for the 'breast is the only way' brigade.
Yes, it probaby would have got better but a few weeks is a very long time without sleep and at what cost to my mental health?
I had a very hungry baby and the formula was thicker and kept my baby fuller for longer.
With my second child I used formula from the start. I received criticism from the midwives and strong encouragement to breastfeed but i held firm as I knew that it was best for me and I knew that my baby would be fine.
Both kids are grown up now and are healthly and happy with good immune systems and no allergies!
I think 'happy mum, happy baby'.
You don"t have to justify yourself to anyone, do what's best for yourself in this situation, and that in turn is what's best for.your baby.
I, myself, am one of four children, all bottlefed and all healthy.
(Trick for putting sleeping baby into cot - warm the bedding slightly with a hot water bottle!)
Best of luck xx