You can sue the person, who would then turn the papers over to his/her insurance company to defend.
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I am licensed in Nevada, but this answer should apply in Texas as well.
You can sue the at fault driver at any time if he or his insurance company do not compensate you for the damages he caused to your car and/or body. His insurance company has a duty to investigate the claim before making payment. He has a duty to cooperate in the investigation. You should file a self report of accident (you may be legally required to do so.) You can go to this site (which, I understand, is for a different city than you live in but will provide a starting place) to find information on the self report: http://www.parkertexas.us/index.aspx?NID=120.
If you choose to sue him, you will have to do so in the court of Jurisdiction. You should consider retaining an attorney if the case exceeds the small claims limit.
Hope this helps.
/s Donald Kudler
This answer does not create an attorney client relationship and does not constitute legal advice, but is solely the opinion of a Nevada Attorney.
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