Is this LEGAL!?! OB question...?

Due to money issues & WIC taking FOREVER, I am just now finding a doctor for my pregnancy. I am between 20-24 weeks. One of the 5 OBs on the list (the one I really wanted to go to) Denied me because I am too far along. Is that even fricken possible? Are you serious?! I can't believe it so now I'm stuck with a fat black guy as my OB and I really don't feel comfortable with a guy down there... unless my bf but anyway. HELP!