What is the best medical school in Florida for psychiatry and neurology?

First, as a fellow high school student in Florida, let me say: I'm am so, so sorry you have to stay here.

Anything that deals with science, pretty much, I would recommend UM. Their labs (and lab programs) are supposedly the best in the state, or so says everyone I've ever talked to who has attended school in FL or is currently looking into it. The only other "prestigious" university I can think of that offers a program like that is Stetson University (private college in Deland, near Orlando; it isn't really known for its science program, though), but it only offers psychology, not psychiatry or neurology. But if you can't make it to either of these I've heard good things about USF as well, and of course UF is widely known.

Good luck, it can be tough to find good schools down here!

Medical schools do not teach a medical specialty.  All physicians have the same basic medical education before continuing their training in a residency program to learn a specialty.  In any medical school your classmates will be future pediatricians, cardiologists, surgeons, etc.

As a resident of Florida you'd pay the lowest tuition at a Florida medical school, so it's by far the best choice to make.  Once you complete medical school you no longer pay any tuition.  In your residency trainign you begin earning money, so you can pick any residency program in the US.  If you want an idea of where the psych residencies are (and they're all over) you can research them here: https://freida.ama-assn.org/Freida/user/viewProgramSearch.do