In Texas, other than the exemptions listed by the FLSA, are there any other reasons an employer can get out of paying overtime?

I suppose it is possible, that your employer is not covered by the Fair Labor Standards Act (FLSA), which could be true if she does no business outside the State of Texas, including purchasing goods or services, or makes under the statutory threshold in gross revenues which, off the cuff, is about $300k.  If she is covered, "not offering overtime" is not an option for her.  There are no unique Texas exemptions as the FLSA is a federal law. You can address your failure to pay overtime complaint to the US Department of Labor - Wage and Hour Division.  There are offices in each of the big cities in Texas - DFW sharing one in Arlington or you can contact a private attorney with experience in labor and employment law.  See www.tbls.org for Board Certified Labor & Employment attorneys.