It seems "probably not" but do you have any group STD and/or medical coverage through your employer or an individual STD and/or medical ins. policy?
Florida is a no fault state: Under no-fault automobile insurance laws, the good driver does not have to prove that the crash was somebody else's fault before getting compensation. His insurance company picks up medical bills, rehabilitation costs and lost wages up to the amount spent. The tradeoff is the injured person cannot sue the other driver for pain and suffering, emotional distress and inconvenience. (If you live in a no-fault state, the no-fault portion of your auto insurance policy is usually called PIP or Personal Injury Protection.) Do you have PIP on your ins. policy?