Often, yes. Your own uninsured motorist coverage is designed for exactly this situation and frequently applies to hit-and-run crashes, which means you may be able to recover for your injuries through your own insurer even if the driver who hit you is never found.
Prompt action matters. Report the crash to the police and your insurer quickly, because hit-and-run and uninsured motorist claims often come with strict, short reporting requirements. Write down anything you remember about the vehicle, and look for witnesses or nearby cameras.
Even though it is your own policy, it is still a claim against an insurance company that may resist paying full value. Knowing the rules and deadlines protects the coverage you paid for.