Legal Question in Personal Injury in Texas

If it was her car in her name, then no. If it was your car, then possibly.

If she is driving your car at the time of the wreck, yes if she has a bad driving record. If she does not and is driving your car then whe would be an additional insured under your policy and your insurance would have to defend and indemnify her. If she is driving her own car, then probably no liability for you since TX does not have the family purpose doctrine and there is probably no coverage under your policy.

To be on the safe side when she gets sued, send the suit to your insurance company and ask them to defend and she should go to a lawyer who specializes in PI to see what he thinks.