Below is a copy of the applicable statute (the current one, not the 2006 statute). If a final conviction was entered on the case, the only way to remove the matter from your record is via pardon from the Governor. A person convicted of a felony can never possess a firearm under federal law. Good luck.
Sec. 49.045. DRIVING WHILE INTOXICATED WITH CHILD PASSENGER. (a) A person commits an offense if:
(1) the person is intoxicated while operating a motor vehicle in a public place; and
(2) the vehicle being operated by the person is occupied by a passenger who is younger than 15 years of age.
(b) An offense under this section is a state jail felony.