I agree with OneBrightGator. I have always felt that the tourist guided cenote dives in Mexico can give an ow diver a false sense about cave diving, I don't want people to say well I did it in Mexico so I can do it here. Ok, down from my soapbox, and on with some info....
You can get a guided intro level cave dive with a cave instructor, however you need to be cavern cert to do so. The best you could get being an ow dive is a guided cavern dive by a cave instructor.
There is a lot of info that you learn in a cavern course, all of which will be used in a cave course, and the cave course obviously goes beyond cavern training. A cavern course can also make you a better ow diver because of the bouyancy and trim and finning styles that you learn. I would recommend a cavern course to anyone, even if they aren't interested in cave diving. I did meet a guy one time that was in acavern course and turns out he was claustiphobic (sp?), needless to say he couldn't finish the course.
If you are interested in taking a cavern course PM me and I can recommend some instructors for you. Also where in Florida are you located?