Every car in New York is required to have at a minimum 25/50 in uninsured motorist protection. This means, if you are involved in a hit and run accident or if the vehicle that caused your accident does not have any insurance, you can make an uninsured motorist claim (your claim for pain and suffering) with the insurance carrier for the car that you are in when the accident occurs.
If you are not in a car, such as a pedestrian or bicycle accident, you can make that claim with the auto policy of any relative resident. These claims are generally easier and faster to process than a typical 3rd party claim (claim against another person for their negligence).