There are relatively few state universities that offer significant merit scholarships. There is a composite thread on CC discussing those schools if I recall. Alabama is well known for that and you would qualify for outstanding merit aid there.
For LAC’s you would need to go to a second or third tier (in terms of selectivity) in order to get large merit aid. However, many of them are “in the middle of nowhere” as you say so they may not be an improvement over your state school in that regard.
Does your state school have its own medical school? I ask because that is the most likely medical school you will attend. State medical schools tend to take a lot of students from their own system so they might have more opportunities than you think. Make sure you have vetted that before ruling them out.