What is the limitations period for a lawsuit claiming damages for personal injury due to negligence to be filed against a city or a county in Texas?

Woman was arrested for a DUI, placed in a holding cell overnight by Houston police, and fell from a high bunkbed and struck her head on the concrete floor, and suffered significant head injuries which are still causing headaches and other problems, six months later. She is challenging the DUI, claiming her impairment was due to a prescription drug interaction. In any case, she says that she several times requested that she be taken to a hospital after the fall, but personnel at the city jail refused to do so.