The other person was clearly at fault, but they are not going to file a claim. Will my insurance contact the driver for damages, or will my insurance cover it?
In Florida, you are required to have what’s called personal injury protection (PIP). This coverage kicks in if you are injured in an accident. Your insurance company will pay up to your specified limit for your injuries. When it comes to property damage, however, the at-fault driver will be responsible for the damages and their insurance should cover the claim.
Have a look at the link below for more information about filing claims after an accident in Florida.