Texas is a "fault" state where the driver who caused the accident and their insurance company are responsible for paying for damages and medical expenses. If you have not yet reported your accident to your insurance company, you need to do so immediately so that an insurance adjuster can take over your case and the accident investigation. This person will review the police report and speak with you and any available witnesses. As the injured party, you do not need to investigate the matter on your own. Instead, use this time to recuperate.
Once the insurance adjuster finishes evaluating your case, he or she will contact you to outline the next steps you need to take. Unless you were behaving in some fashion that would have made you more than fifty percent responsible for the accident, such as driving while intoxicated or distracted or driving at night without headlights, then the police report that outlines that the other driver was at fault along with your statement, witness testimonies and hospital details should be enough to convince your insurance company that you were not at fault. If this is the outcome, you benefit greatly because the driver who is at fault typically experiences an increase in their insurance premium costs.
Who pays for the damages and medical bills depends on whether your insurance company or the police can locate the other driver. Or, your policy might include extra personal injury protection where your insurer pays part of the costs while it tracks down the other driver and that driver's insurance company. Of course, these scenarios do not always go smoothly. If your insurer says that there is nothing it can do, you should contact an experienced professional local auto accident or personal injury lawyer to pursue the matter further in court.