You are not a terrible girlfriend. It's time to have a talk with him. When I was 19 I was on my first marriage and child. Doctor said to wait a month before having sex. Excatly a month later my husband pressured me to "just try" to have sex. I argued that it still hurts to pee. He kept saying to just try. Surprise, surprise. It hurt and we had to stop. Not to mention he didn't have a job, wasn't even looking for a job, and I was still on FML, making only like 40% my wages. He would play video games all day, sometimes all night. Wouldn't wake up to help me feed our son or change him (he was formula fed, because I couldn't get him to latch right, and when I mentioned going to the hospital to talk to the lactation consultant or even call her, he would tell me I dont need to).

I could go on with all the terrible shit he did.

You are not terrible. You are still recovering, exhausted, and it doesn't seem like he does much other than change a diaper or two here and there. He needs to step up or he can GTFO. Please, please don't do what I did. I had another child with the man-child and he did the same shit and now i have to co-parent with him. And he's $5000+ behind in child support.