If my vehicle was hit by a driver excluded from the insurance policy of the car he was driving.

As I am licensed in Florida and Vermont, I cannot offer you specific legal advice as to Texas state law. However, generally, in a situation like this, you would generally turn to your own medical payments coverage or uninsured motorist coverage in your own automobile liability policy. If you do not have either of these coverages, then you will be in a position of having to sue the adverse driver for your property damages and medical bills. You should determine the statute of limitations in Texas for bringing your type of claim and make sure that you either settle the dispute with the adverse driver or file suit before that time limit expires.

I would appear the driver is probably uninsured. Hopefully your auto policy includes uninsured motorist coverage on your vehicle. If so, your insurance carrier should provide coverage. You also have the right to go against the driver directly although that is not often successful in that it can be difficult to collect. Another possibility would be to sue the owner of the vehicle for negligently entrusting the vehicle to the driver. In that case you would have to show that the owner knew the driver was a poor driver and entrusted the vehicle to him/her anyway. Generall, in Texas, you must bring a claim within 2 years if you are an adult of sound mind.

If he has no insurance, it will be difficult for you to recover anything on the case. You may try to determine if he has his own car. If he does, his insurance may still cover him when he drives another vehicle. The other option would be Uninsured motorist coverage. If you do not have it on your policy, try checking with family members that live in your same household. Their UIM insurance will often cover you if you don't have it on your policy. Your last options would be to pay an attorney by the hour to bring the claim or file suit on your own behalf in small claims court.