Are there time limits to sue for injuries in an accident case?

Yes, there are. There's an applicable statute of limitations which is a deadline for filing suit in any case involving injury or death. In Florida the personal injury statute of limitations is 4 years from the date of injury or death. In wrongful death cases, the statute of limitations is 2 years from the date of death. In breach of contract cases such as uninsured motorist actions, it's 5 years from the date of the accident.