Apply to Auburn and Alabama as soon as applications open. Quick turnaround, no essays. If you want to be a doctor, go to one of these. Grades and MCAT are critical for admission to medical school. Both of these will be extremely affordable and will allow you to conserve your assets for medical school. You are also fortunate to have a top-tier in-state medical school in UAB. This would be my preferred path for you if you decide to be a doctor.
The difficulty is the schools that are best for engineering may not be best to get you into medical school so it would be good to have a path before you apply. As far as your state schools, Auburn has a top 30 undergrad engineering school so if you remain undecided that might be a good idea although I’ve heard great things about Alabama engineering as well.