If Tulane’s not too far from home, then you should also consider Xavier (LA). It’s an HBCU with a great premed program, and though it doesn’t have a med school yet, one is in the works. It’s also part of a consortium with other New Orleans schools like Tulane, Loyola New Orleans, and Dillard whereby students can take classes at a different school for the same cost as at the home school.
Closer to home, Morgan State is also opening up a med school. It’s part of the Baltimore Collegetown consortium with Johns Hopkins, Loyola Maryland, Goucher, and Towson, among others.