Yes, you can still file a claim even if you were not wearing a seatbelt during the accident. However, not wearing a seatbelt can negatively affect your ability to recover compensation.
Under Texas law, if your failure to wear a seatbelt contributed to your injuries, then the amount of compensation available could be reduced accordingly. If your injuries would have occurred regardless of whether you were wearing a seatbelt or not, the defense would not apply.