I had a very similar experience and felt like I had failed for the same reasons. The above advice is good re speaking to a doctor - I just thought it was more of the same, failing now to cope with my baby, and didn’t get help but honestly it made me hate maternity leave. Then I felt like I’d failed at maternity leave because I should have loved it. So definitely speak to someone to work through those feelings and of course you’re 100% not a failure. The first 4-5 months PP were the hardest but you will get through it. Had you considered having your baby checked for tongue tie? Ours had a posterior one that wasn’t caught at the hospital (they’re not qualified to diagnose it anyway) and when we had it snipped she was feeding way better (still not BF but better bottle latch) and the colic went away. Not the main point of your post but just asking because I could have written this post myself when I was 2 months PP
You are not a failure birth is unpredictable. I would suggest going to see a cranial osteopath. That will help your son by helping align him and release any tension - this along with getting a tounge tie checked will really help baby. May even be good for you too as the trauma of birth is stored in your body it can help release that too. Things will get better.
Oh babe you haven't failed! You really really haven't! Having a C-section isn't failure, and neither is using formula. He's here! He's fed! He's loved! That's all he needs. It sounds like you could use some support. Could you talk to your GP and/or someone in your life about how you're feeling? You might just be overwhelmed (it's overwhelming!) but you might also have PPD, and it can't hurt to get that checked out. You have SO MUCH time with him. I know these early days feel incredibly significant, but I currently have a newborn, a 4yo, and an almost-8yo, and I barely even remember the older two's infant days. This is not the only time you have, and it's going to be ok.