If you have not yet called the police and reported the hit and run you should do so as soon as possible by contacting the local law enforcement agency so they can investigate. With the license plate number you have for the at-fault driver in the hit and run, hopefully the police can track down the vehicle owner.
The Texas Department of Insurance advises that your uninsured motorist coverage will pay for your damage in a hit and-run accident only if the accident is reported to the police. Even without you having this type of coverage it is likely if you find the at-fault party that their insurance company will require a police report on the incident.
If the driver is found and the vehicle owner takes responsibility then you should be able to place a claim with their insurance provider. If instead the police are only able to locate the owner of the vehicle then you may need to check with the Texas Department of Public Safety to see if they will release information on the person's insurance that is on file with them.