Yes, you can. You may be asking this question because Florida’s a no-fault state, and many people misunderstand that term to mean that you can’t bring a claim against an at-fault driver because it’s a no-fault state. But what that really means is that your own insurance will step up to the plate and pay for the first part of your medical bills, but you can still bring a claim against the at-fault driver for all of your injuries, even if you don’t have insurance.