No way you should pay full rates vs going to UF. You need to shop around for either need-based aid (offered at more selective schools) or merit based aids.
You need to run the Net Price Calculators at a few schools. Your grades are good enough that you have a shot at some selective schools that would offer significant amounts in need-based aid (grants), particularly if your family already has several other children in college.
Try out Vanderbilt’s, as an example:
https://npc.collegeboard.org/student/app/vanderbilt
Next, look at schools that offer merit-based aid. Zinhead’s link is a good start.
Good Luck!