If you mean that you successfully completed your deferred adjudication period for your DWI, then yes - you are eligible for something called Non-Disclosure.
A third DWI in Texas is a felony. Non-Disclosure is available for certain Felonies ONLY if the you have successfully completed your deferred adjudication period (also known as community supervision). If the period of deferred adjudication was successfully completed, you can petition for an Order of Non-Disclosure, available after FIVE years from date of discharge and dismissal (i.e. successful completion of deferred adjudication).
You could not have had a deferred adjudication on the 3rd DWI as deferreds have not been available in Texas for DWI since either 1982 or 1984.
Moreoever, you cannot seal a record of a DWI. It is one of those types of cases excepted from the rule.
You are lucky if the priors are not showing up. Perhaps you got deferreds on those & whoever enters the records was just confused.
Congratulations on your success in staying clean & sober, though. That is a huge deal - many people do not realize how hard that is on a daily basis.
I'm sorry there is nothing more (other than an unlikely pardon) that can be done to clear your record.
No. Expunction is not available for a felony conviction. Successful probation completion is irrelevant and there is no deferred for DWI, in Texas. If you were placed on probation, after 1982 for a DWI, it is a final conviction and not expungable. The only way to get it cleared from your record is to obtain a pardon from the Governor of the State of Texas.