If he's too immature to understand that this is his child and his responsibility, in sickness and in health, then he's too immature to marry, for better or worse, in sickness and in health.
If you think you still want to marry him, you both need a lot of serious premarital counseling before you put so much as one toe on the road to planning an actual wedding. He needs to grow up and man up. Taking a sick infant to a wedding? Everyone there would have gritted their teeth and he would have thought they were smiling when they were furiously trying to avoid you all. You did the right thing to stay home.
Meanwhile, you're still stuck with him doing exactly what he pleases, when he pleases, like a self-centered teenager. Sorry, that's not fair to teenagers -I've met teenage boys with more sense of responsibility.
The fact you say you "feel like he doesn't hear me when I speak up" and you feel depressed is very significant. First talk to your doctor to be sure you don't have post-partum depression, but even if you do, your fiance still is an issue.
Find a time when you can leave the baby with a friend, and a place where he won't be distracted (no phone, his cell or Blackberry is turned off, the TV's not on, you're not at dinner so he can't stare into his burger) and tell him point-blank: You feel like you are a single parent. Your job is school and it's vital to your child having a better life. He is not respecting you or your relationship by failing to help you do your job, study, or by failing to help you keep your sanity by getting out occasionally. You love him but need him fully engaged and that means being with his child. Tell him you feel he doesn't listen to you and that you want to work out a schedule for both of you -- the days and times he's with the baby so you can exercise and study. Having a specific schedule may help him focus. Have paper and pen ready and if he gets balky and says "Oh, that's so formal, I'll just help out when I can," tell him you need the certainty of specific amounts of study time on specific days so you don't fall behind in classes, and your gym schedule requires you to set times and days. Then tell him part of that schedule is parenting classes for you both, and have that class schedule ready and waiting so he can't make excuses and put off finding out about such classes. "Here's all the information, and I know your work schedule and this will work with that schedule. We start on Tuesday." With a big smile because this new schedule and parenting class thing is great, right?
Either you can be a single mom to both an infant and an overgrown teenager, or you can be a single mom just to an infant once you leave him. He's currently just "playing house" when he wants; you live it every day. Good luck.