Just moved to " tropical" South Florida, my shower has mold!!!

Not enough air circulation in your bathroom. Do you have a ventilation fan? If so, you may need to have a stronger one installed and be sure to run it while you are using the shower as well as after you are finished. If you don't have a fan installed, you should have one put in and be sure it is vented properly to the outside, not just into your attic space! Also you will want to remove all stained caulk and redo using caulk specially made for showers and tubs. It sounds as if someone may have just recaulked over existing moldy caulk in the past rather than taking the time to do it properly and remove the bad caulk and clean with mold killer before recaulking.

Keep area well ventillated

Clorox does not kill the mold.White vinegar or this....https://www.hometalk.com/diy/clean/bathroom/the-best-way-to-remove-mold-mildew-with-2-ingredients-no-bleach-33077514

Vinegar, vinegar, vinegar! Vinegar kills mold spores, bleach does not - improve ventilation - use the exhaust fan, install a better one, crack a window, even a portable fan will work.

http://restorationmasterfinder.com/restoration/what-kills-mold-bleach-vs-vinegar/

https://www.networx.com/article/bleach-vs-vinegar-mold-removal

My pleasure.......

Wash it with bleach water to clean the mold up and perhaps to lessen staining. Spray the entire area once dry with vinegar and let it dry. Vinegar with its antibacterial and antifungal properties will help keep the shower from growing so fast. Now you just need to figure out how to keep the humidity level in the bathroom to a minimum. That can be a problem in South Florida where it is always humid. I lived in Naples, Florida for five years and mold, mildew and algae grow everywhere so easily!

You should also look at striping and repainting with mold resistant paint