Yes – but it might not be easy.
Under Texas law, if the accident was indeed the other driver's fault, you can pursue a claim against the negligent motorist’s liability insurance company to pay for your car's damages and your injuries.
The fact there were no tickets issued and no accident report made does not prevent you from making a claim - it just makes it a little more difficult to prove, which is why it is so important that you consult with a board certified Fort Worth personal injury attorney as soon as possible. The sooner you have an experienced lawyer on your side, the better your chances of recovering the maximum possible compensation.
Police officers have great discretion on issuing tickets and our attorneys routinely see accident reports completed with an assignment of fault but with no ticket issued (even when one could have been written). Also, if the cars are able to be driven from the scene and no one has to go to the hospital in an ambulance, then the investigating police officer often doesn't write up a report and merely facilitates the exchange of insurance information.
So don't let the lack of a ticket or a report deter you: If the accident was not your fault, you should not be penalized. You don’t have to be stuck with huge medical bills, the cost to get your vehicle repaired or replaced, or any other accident-related expenses. You have the right to recover full and fair damages.