Probably not. Under Texas law, you can only get an expunction of your record under very limited circumstances. Unless you were pardoned or your conviction was otherwise overturned, you are not entitled to an expunction. Under certain circumstances, though, you might be eligible for a court order of non-disclosure, which would prohibit the Department of Public Safety or other agencies from releasing the records of your conviction, except under certain circumstances and to certain people (like law-enforcement personnel, for example). If you successfully completed a deferred adjudication probation, you could be eligible for an order of non-disclosure two years after your date of discharge (for misdemeanors) or five years for a felony.
I Have An Old Criminal Conviction. Can I Get It Expunged?