If you did time, then it is a conviction and there is nothing short of an unlikely pardon that you can do. If you successfully completed a deferred adjudication probation and you have had nothing since that case, you can petition the court to seal your record.
The only way that you would be eligible for an expunction is if this case was dismissed. It does not sound like it was dismissed. If you were offered and successfully completed a deferred adjudication you may be eligible to file a petition for non-disclosure and have the record sealed. Unfortunately, if you were convicted whether you served prison time or was given a "straight" probated sentence, you are not eligible to have your record expunged or sealed in a petition for nondisclosure. The only option that you would have in this case would be to petition the Governor of Texas for a pardon. Unfortunately, you probably have a better shot of winning the lottery than receiving a pardon from the Governor.
If you received probation you may be eligible to seal your record. It depends on whether you received Probation, or a special type of probation called deferred adjudication. If you completed a deferred probation and have not gotten into trouble since, you may be eligible to have your record sealed. If you did time, or took a plea just to get out of jail, then you have a final conviction and your record is unfortunately permanent.