If you were a passenger in a car accident you absolutely can file a personal injury claim and you can file it with whoever was at fault for the crash.
If the driver of the car you were in was at fault you could file it with their insurance company.
If the other vehicle is at fault you could file it with their insurance company and if both parties were at fault you could file with both their insurance companies.
If Uber or Lyft was involved, you could file a claim with them and if the person who caused the crash doesn’t have enough insurance you can even file a claim through your own insurance company under your uninsured or underinsured motorist coverage.