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If DPS already said no then I think you have your answer, but here's the law.

GC §411.172. ELIGIBILITY.
(d) For purposes of Subsection (a)(7), a person is incapable of exercising sound judgment with respect to the proper use and storage of a handgun if the person:
(1) has been diagnosed by a licensed physician as suffering from a psychiatric disorder or condition that causes or is likely to cause substantial impairment in judgment, mood, perception, impulse control, or intellectual ability;
(2) suffers from a psychiatric disorder or condition described by Subdivision (1) that:
(A) is in remission but is reasonably likely to redevelop at a future time; or
(B) requires continuous medical treatment to avoid redevelopment;
(3) has been diagnosed by a licensed physician or declared by a court to be incompetent to manage the person's own affairs; or
(4) has entered in a criminal proceeding a plea of not guilty by reason of insanity.