If you carefully roll your clothes they won't get too wrinkled. You can put them in a trash bag to keep them dry, which is the cheapest route, or spend more on dry bags or water proof panniers. Keep anything you can at work, like shoes, for example, that take up space in your backpack/pannier or whatever you are using to transport things.

If I were you and had a locker room at work, I'd just get wet in Florida temperatures. The challenge is to get everything dry by the time you need to put it back on to go home. If you are lucky you will have a place to hang things with a fan nearby.

There's nothing that's waterproof and keeps you from overheating when it's warm. A waterproof jacket with pits zips is the best I've found, but any material that keeps water out won't breath.