Typically a person doing a background search will see the arrest and the dismissal. You can probably get it sealed in the State of Texas. I recommend speaking to an experienced criminal defense attorney to help you through the process.
Attorney answers to questions are for general purposes only and do not establish an attorney-client relationship. Please contact at the Law Office of Daniel Corno, (832) 767-2922, 1535 South Richey, Pasadena, Texas 77502 email@example.com, elabogadodaniel.com
What you are most likely entitled to is an "order of non-disclosure" which technically does not take it off of your record but can keep it from coming up on public background checks like it does now.
A lawyer will be able to check your specific case resolution and tell you how completely they can conceal the history of your criminal record.