First of all, med school is gonna cost 400K, so you really do want to keep the cost of undergrad down. I realize both your parents are docs, but do they really want to spend close to 800K on your education, when you could get to the same result for much less?
You do have a slight hook - that is geography. Not so many great applicants coming out of Alabama, and schools do want geographical diversity. Also, as a woman going into engineering, you’re desirable to maintain sex balance.
Med schools DO want engineers, especially bioengineers. They realize that docs with engineering degrees are the future designers of biomed devices. I remember a med school recruiter (wow, think of that) coming to my Ivy’s engineering school (but back in the old days) and specifically inviting the engineers to apply, for just that reason.
You might get massive merit money at state U’s with engineering seeking high stats students. U Arizona comes to mind, but look for the recent thread about schools with lots of merit money for high stats students. If you made Nat’l Merit semifinalist, even better. These schools would probably be your best bet. They will look at your high stats, and want you. You might even get a full ride, and if not that, quite likely to get full tuition.
If money is truly no object (and honestly, even 2 doc households don’t fall into that category), then add MIT for highest reach, maybe RPI (they’ll give you enough merit money to match your in-state cost). But I’d recommend going with the big merit money at the state flagships seeking students like you. Med schools will be happy to take you from those, assuming your academic achievement continues along your current path. And you’ll save your parents a ton of money.