Can the other driver's insurance company delay paying for my car repairs to pressure me into signing a release on my injury claim?
No. The Texas Insurance Code prohibits this unfair settlement practice.
You have the right to settle the claim for the damage to your car before you settle your injury claim. Normally, you should wait to settle your injury claim until you are released by your doctor.
Insurance companies which engage in this unfair tactic may be liable for any damages which this practice causes you as well as for your attorney fees.