Well, the good thing about newborns is that they sleep... A LOT. So they're not terribly tough until they're a bit older and they're awake more of the time. So you have some time to get yourself together and remold yourself back into the man you once were. I am working on it as well, although with a different situation. I, too, am a father - I have a 5-year-old daughter. It is anxiety-inducing, it truly is, but you need to let the medicine settle, you need to work on YOU as well, and possibly see a therapist to expedite your recovery.
Channel your negative energy into something positive. When I was depressed a couple of years ago, I started to exercise... Seriously exercise. This helps relieve stress, brings up your confidence, and actually gives you energy. You don't even need a gym to get started! Start with calisthenics. Clean up your diet, too. No more junk! Look into some nutritional information. I also suggest, as always, supplementing with Fish Oil (Some people say it helps with depression). I take 2g or so a day in capsule form.
You're not a bad person -- I can tell through your post. Your heart is in this, but your mind isn't in sync with it. I've been there as well. You need to work on you, but do your best to be there for your baby. Even small things that take minimal energy will show your future wife that you do, in fact, care. Even take her to a therapist WITH you to have a professional sift through all of the facts and lay them on the table with her there. But small things like... I don't know, vacuuming, washing the dishes, tidying up, etc. is helpful and beneficial.
I wish you the best of luck.