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.
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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.