Driving records are managed by the Department of Drivers services under the Executive Branch of Government for the State of Texas. The Judicial branch has nothing to do with those records and generally expungement is not an option. Having the records sealed is also not likely an option. Time is your best friend as it is like your credit report. Infractions drop off as time passes.
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Under certain circumstances you can get records of criminal charges expunged in Texas. Under some others, you may be able to get an order of non-disclosure. But, this has to do with criminal offenses. Most traffic tickets are actually criminal offenses in Texas. Bottom level misdemeanors, but still offenses.
Other stuff that may be on a driving record, like accidents you have had, administrative license suspensions, things like that, are not going to be crimes, and so expunction and non-disclosure are not even on the table.
As always, the best approach is to make an appointment with a lawyer who handles the area of law you are curious about - here tickets, expunction, and non-disclosure - and discuss the details of your situation.
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