Texas does not allow misdeanor convictions to be expunged. But, any type of a misdemeanor that is dismissed prior to trial or to a plea bargain may be expunged. If you were charged with a Class C misdemeanor and received deferred adjudication with the charge later being dismissed, that offense is also expugnable. Also, if you went to trial and were acquitted it would be expungable.
The requirements and process of expunction in Texas is found in the Code of Criminal Procedure. §55.01.