You absolutely can hire a lawyer even if you live out of state and it's the right thing to do since your accident occurred in Florida. If you're here on business or pleasure and you have an accident, your case is going to be handled here in Florida. The insurance company, the adjuster, and the witnesses are located here. You may go home and receive your medical treatment but your case is a Florida case. And, with that being said, no one understands how to handle a Florida accident case better than an experienced Florida attorney.
Many people often make the mistake thinking they can go home and hire a lawyer from their hometown. The problem with this is even though they handle accident cases in their state they will not be able to file a lawsuit in Florida which means that they would have to take that extra step to hire a Florida lawyer to get that done. And, not all cases turn into a lawsuit but if it does and you need the claims adjuster to believe that you're willing to file lawsuit in ordered to get it settled properly, you might need that leverage of having an attorney here where the accident occurred.
The other issue may be that an attorney who is experienced handling cases in their state and does a great job still may not know all the Florida laws. This is another reason why it might be in your best interest to hire a Florida attorney from the very beginning.