It would help to know how old your babe is, and how early. But that's kind of for specifics.
In terms of the crying - I'm not sold on "it isn't PPD, it's just normal post-partum stuff" thing. If it's making your life more difficult, get help with it now. Mothers of premature babies frequently suffer from depression and anxiety, which is why NICUs so often have social workers on staff. When my daughter was in the NICU, they were able to send a counselor to sit with me by her crib and talk to me. It really helped. I would ask the staff on the unit what resources there are.
Second - oh honey, I could come slap your nurses for you. Really. It is your baby. You should be taking some kind of possession. DON'T BE AFRAID TO STEP ON THEIR TOES!!! I agree with the suggestion that you talk to the neonatalogist in charge of your son's case and get orders written into his chart regarding holding. I will warn you that some NICUs leave these decisions up to the nurses, in which case, you want to find the nurses most up-to-date on and in favor of kangaroo care and recruit them to your case. The process of going from isolette to arms and back again is exhausting to babies, but being in your arms is good for the babe. You don't want to be taking him out and putting him back all the time, you want nice, long stretches in the recliner chair. (And if your son is on bili lights, or a respirator, they're right to limit his time out. If not, full speed ahead with kangarooing.) If the doctor's advise nursing at every other feeding, that is a pretty aggressive schedule for a preemie (we started off at once a day), but absolutely get it written in his chart and try it. They can always top him off via gavage tube.
My daughter was born at 32 weeks, and while she was in the isolette, they encouraged us to lay our hands on her - open the port holes, and cup the top of her head and her legs and feet with our hands. You want the touch to be gentle, but steady. No stroking, because that does upset the baby at this stage. Just hold. You should be able to do that even if your son is asleep.
I would encourage you to fortify breast milk. Most babies spend the last trimester building up stores of fat, and preemies don't get the chance. The more fat they can layer on, the easier time they have regulating body temperatures, so we do try to get as many calories into them as possible. We supplemented until DD had been out of the womb for about three months, and then we were able to stop. Some people carry on with it longer.
I know this is hard, mama. Hang in there - it will get better.