Oh bad/good I feel your pain! There is enough to deal with with recovering from c section, learning how to care for a newborn, sleep deprivation etc and breastfeeding is ok if it goes swimmingly but really awful if not. You are awesome and doing the most awesome things for your baby. But it sounds like you need more help. I don't want to tell you what to do but here is where I am if it helps to know.
I'm still in hospital - taken down a notch from high-risk pre-eclampsia watch and got the uterus infection under control. However, they are now worried about H, who isn't weighing enough. Despite lots of pumping my colostrum is all gone (into her, thankfully) and my milk has not come. Literally, four sessions of full on pumping and everything is dry. We are all pessimistic that it will now come in in the right quantity. So we are on a strict feeding regime with formula to build her back up again. It has made the world of difference. I was really struggling, losing lots of weight myself. Even when given the chance for a nap I wasn't sleeping or was having hallucinatory nightmares instead. I feel bad about not bf, but not as bad as when I realised that my mental health was In danger of being compromised.
I know it's a fraught area; but it helps that I know several formula-only babies who are thriving. And I've given her the best bit with my colostrum. I still feel sad that I'm too scrawny and poorly I can't do it by myself, but the important thing is that baby gets fed and I stay on an even keel.
I repeat - simply by keeping that baby alive you are doing the most awesome thing. And formula is not evil! If circumstances dictate you have to change from your original plan, it is not your fault and no guilt should attach to it.
Massive hugs to you and two fingers to anyone who says its unmumsnetty.