What do you plan on doing with a BioE or BiomedE degree? Both are limiting majors, job-wise.
With your stats, Alabama would give you free tuition. As an E major, you’d also get 2500 per year. You’d also get a Pell Grant. If necessary, you’d get a small loan. Run Alabama’s NPC. The results won’t mention the E scholarship, so take that into account. Also, at Bama, you can reduce your cost further by choosing a “standard double” dorm…rather than the expensive “private room” dorm cost that is included in the cost estimate.
This could be your safety.
Alabama doesn’t have BioMedE…but it does have Chemical and Biological Engineering and it does offer some BioMedE classes. Chem&BioE as well as MechE are fine substitutes for BioMedE majors. Any BiomedE grad school would certainly accept ChemE, Chem&BioE, and MechE applicants as well.