My sister has bi-polar disorder. Since she is not considered in remission by a doctor, the state will not issue her a CHL.
HOWEVER, Arizona issues out of state, non resident licenses and as far as mental health goes, you have to be committed against your will, or be considered a danger to society or yourself by a JUDGE, before you are excluded from obtaining a license. I would look into an Arizona carry license which is valid in Texas. I'm getting my sister working on it so she won't be victimized.