If you were convicted of a non-violent felony in Texas and if you received it was a deferred adjudication ending in the dismissal of your sentence after probation, and you meet the other statutory conditions listed in section 2 of the link below, you can apply to get your Texas record expunged. Otherwise,Texas will expunge convictions which have first been pardoned by the governor.
Here is the Texas Expungement Law
. If you are eligible, the link will explain how you would have to proceed in section #5. You would have to petition the court. You would not need a lawyer to file for an expungement, if you were comfortable doing your own paperwork and appearing in court on your own behalf. There are, however, lawyers who specialize in expungements and pardons.
If it turns out that you don't meet all of the conditions necessary for an expungement, then you'd have to apply for a pardon. Getting a pardon is very difficult, but if you have been out of trouble with the law since 1978 and even were given special clearance at one point, you would have a much better chance than most to obtain one. Once you were granted the pardon, you could then go back and petition the court for your expungement, for which you would then be eligible. You could do this yourself as well.
The Texas Board of Pardons and Paroles
screens all of the applicants for pardons for the governor. I have linked you to their site where you can find more information and downloadable forms.. No lawyer is necessary. The pardon doesn't erase your conviction but it is official recognition from the state that you've turned your life around. So it's worth having even if should you decide not to bother with an expungement.