JustHolly, having seen what Andrew did, if it is a threat to you, I would leave. Make a motel reservation in some city which is out of the path of the storm, and go there. Or whatever to get out. I woul not want to be around for a cat. 5 storm, especially in a third story apartment.
And if your management tells you the buildings are built to hurricane code or something, I would not be quick to believe them. I know building in Miami has gotten a lot more...well, better, able to survive some winds...but I don't think the rest of the state is that way.
As far as supplies, have lots of water, canned goods that you can eat w/o cooking, a manual can opener, flashlight, battery operated TV and/or radio, extra batteries (get 'em now while you can) , any meds you can't go without, pet food if you have pets, and anything else you can think of that you must have. Oh, you might want to put any important legal papers in some kind of watertight container, and in the safest place in your home you can find. You likely won't have to worry about flooding, being on the third floor, but if the roof went, you'd want that stuff safe. Things of sentimental value too.
That's all I can think of! I'm sure there is more, though, if anyone would like to add to this!