Postpartum depression, but for dads—anyone else?

Our second kid was born 6 weeks ago and I feel horrible. I know that sounds dramatic but I'm not joking. I'm not bonding with the baby the way I did with our first. I feel trapped and resentful, which makes me feel guilty. I keep thinking "this was my choice, what is wrong with me?" My wife is postpartum too and needs support, so I can't dump this on her. It's not depression in the classic sense—more like I made a huge mistake. Has anyone dealt with this? Does it get better?