@theminkin
You would be eligible for a full ride at the University of New Mexico if you are a NMF. Arizona State with its excellent Barrett Honors College also offers very generous merit scholarships for NMF. UT-Austin is more highly ranked than either of these, but if you want to keep costs low and save for med school, they are worth looking into. I know a young lady who got a great deal at UT-Dallas with stats just slightly lower than yours.
Farther afield, there are merit scholarships by separate application at Wash U St Louis and Case Western that go up to full tuition. They are very competitive but you have excellent stats - worth a try!
Case Western (I believe) has a direct entry BS/MD program as does UNM.