While I don't practice in Texas, here is my answer.
Most states are pretty much the same in this area. If you are convicted of a Misdemeanor, it is usually not a complete bar to getting licensed for things like real estate. If you were convicted of a felony, that would constitute a bar.
In either case, most states have what is known as a Certificate of Relief from Civil Disablities (or it may have a similar name or title) which, if granted, would not automatically bar you from getting licensed.
My suggestion is you contact a local lawyer in your state and ask if Texas has such a Certificate of Relief and if so, ask how much it would cost to get one. Usually you can go directly to the Court and ask for the form from the Clerk of the Court and fill it out yourself. However, not all Judges will grant them and that's where you will probably need an experienced attorney to assist you.