Were you a minor at the time of arrest? What was the final disposition of your case? Did you pay an attorney to have it expunged or sealed?
Also, many times it depends on which background search a company is conducting. How did you review your background from TDPS? Have you tried searhcing on publicdata.com? It seems to be a favorite search engine among companies. However, there are countless databases that may have your record and the only way to truly ensure they will not expose your arrest to to file a Petition for Expunction or Petition of Nondisclosure, if you are elligible.
Please feel free to contact me. I need more information to adequately advise you and alleviate your concerns.