Maternity leave

I need help/opinions! I work as a phlebotomist at a hospital since March and a month later I found out I was pregnant. My insurance goes through them and have been paying STD so I can get a check while on maternity. (And so I was told by HR when I signed up) I'm 37 weeks pregnant now and my supervisor decides to NOW tell me that I didn't qualify for FMLA and that if I didn't come back a week after delivery I will be fired! Blew my freakin mind! I seriously didn't have anything to say because these past few months I've been paying for STD just to be told I can't spend time with my first born son and that I have to come back in a week or I lose my job. I'm physically and emotionally not ready to leave a one week old baby. Is there anything I can do?! My husband says it's totally illegal and that I at least get 6 weeks if anything. Thoughts? Opinions? I work full time and sometimes overtime and I was old by other people that this situation didn't sound right at all. People have tried to give me PTO but apparently my boss said it can't be done either.