You mention that you have "proper" auto insurance but did not mention if this was only the Florida state required property damage and personal injury protection (PIP) or if you also have collision and comprehensive or Uninsured Motorist Liability.
If you have the physical damage coverage of collision on your vehicle then you can make a claim through your own insurance policy for the damages the uninsured motorist caused when they rear-ended your vehicle. If you have collision insurance on your vehicle, you can have your own insurance company pay for the damages, less your deductible, and then your insurance provider will usually subrogate against the at-fault party to recover their loss. You may see if they can get back your deductible amount as part of the subrogation process or you can file your own suit against the uninsured driver for damages.
If you do not have collision coverage or do not want to place a claim through your own insurance company your other option is to take the at-fault party to court. If you obtain a judgment against the owner of the car and they do not pay the judgment, you should contact the bureau of Financial Responsibility in the Department of Highway Safety and Motor Vehicles so they can take the appropriate action against the owner of the car.
Florida has the Bureau of Financial Responsibility whose sole purpose is to ensure that people are responsible for their actions involving motor vehicles. This state agency does so by making sure everyone has insurance to pay for the damages they cause, or they may cause, when they own a motor vehicle or register a motor vehicle. This Bureau should help you recover your damages and be compensated for your injuries if you sustained any.
The Bureau of Financial Responsibility will take action to help you. Here is what they need from you:
- Crash Report from a law enforcement agency that investigated the crash. The report must indicate a moving violation charge.
- Obtain this at the earliest and send it to us. Please note that even if you don't, we will process the crash within the next 2-3 months automatically.
- Proceed to obtain a final judgement from a court against the at-fault party and send the final judgement with the crash report to us.
Once you have the obtained a judgement against the other party, it will be immediately enforced and the at-fault party's license, tags, and registrations will be suspended for 20 years or until the entire judgement is satisfied. For more information on this topic you can contact the FL HSMV or the FL insurance regulatory body.