Hi there! I think everything you are feeling is totally normal. I was dealing with depression before I got pregnant and avoiding going on meds for it. My OB actually started me on meds while I was pregnant to hopefully prevent or lessen my chances of PPD. I have been on them ever since, which is now eight years. I'm not saying meds are the answer for you (you obviously know more about that than I do, being a med student!), but I want you to know that you are not alone and this actually sounds normal compared to my experiences in the NICU. You should definitely talk to someone. Even talking with my counselor on the phone was helpful, since she was too far away for me to actually go in while my son was in the NICU. And talk to the people around you in the same situation. I made such good friends with some other moms. We bonded while pumping in the pump room, which I guess you can't do! But there ARE other dads around. It's stereotypical that men don't want to do that, that they always have to be strong, but is it worth your own health to avoid getting help? BTW, avoiding the NICU when you are sick is the right thing to do! You will always feel guilty about something you are doing, whether your kid is in the NICU or not--that's just part of parenting. You just do the best you can do.
Something that really helped me was really trusting the staff. I didn't know anything about prematurity before my son was born. While I consider myself an intelligent person, I knew enough to know that I didn't know anything about this, and these people did, so I needed to let them do their thing. Maybe it was just my hospital, but they were AMAZING. So knowledgeable and professional, while also being hugely compassionate and patient. My son was not just their job, but was really important to them. That was obvious right from the start so it wasn't hard to trust them. You want to be there as much as possible, but you know your son is in the best place for him. Take some time to take care of yourself (and that goes for your wife, too).