It does get better, let me just say that first.
I was in a similar situation and thought I'd made a massive mistake and my life was over, would end up getting a divorce and never seeing my kid again. Crying all the time, struggling at work, not sleeping, mind thinking over stupid things constantly and as you are, being tough on myself for being like this.
Again, like your wife, mine was very supportive which was great. It took me a week to tell her, but the fact I just burst into tears as I held it in for so long, I couldnt hide it anyway.
I was put on some vallium to start with to help me sleep, but that only helped to get to sleep. I would still wake up a few hours later. I was then put on some anti anxiety which kind of helped, but not a lot. Finally I was put on anti depressants and after 2 weeks was getting right back on track. I was refered for therapy too, but I have still not heard anything from them, though now I dont feel I need it.
Our little one is now 2.5 months and things are really good now. She is smiling and cooing back to us and its great. I still have a few moments when I think bad things, but as my head is sorted now, I can process these things and move on easily.
Hang in there, 'everybody is right' it will get better!!