First off, IF I read your post correctly, you didn't say that you didn't make enough to claim him, you were only quoting what the baby's father said. Right?
Do not be mislead into believing that you don't "make enough money to claim him", because, to me, it sounds as though you may qualify for the earned income credit & you probably would get money back. Which, in return you can use to help support your child even more. And you would know more about what your child needs. If nothing else, put the money back for emergencies, doctor's visits, medicines....
Do you live at home with your parents & pay them rent? Then it is possible that they can claim either the child or both of you, if you are still in school & they can show they provided more than half of your upkeep & you lived with them for more than half of the year. That would help them, I'm sure.
If the father is still living at his parents home, then I doubt he is paying more than the bare amount & if that is true, then I doubt that he is paying more than maybe the cost of diapers, if that much.
Honey, take care of yourself & your child first, as you said, you will be there for that child, hopefully the rest of its childhood, if not longer. But, try to get back into school or stay in school. You will help both of you out more with a good solid education. Good luck!