Was charged but not convicted do to medical reasons can they still own a gun in tx of a state felony?

Not sure what you mean, but only a conviction of a felony (or misdemeanor family violence) can limit your possession of a firearm.

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Exception: If a person was found not guilty by reason of insanity, they were likely adjudicated as being mentally incompetent. If so, that IS a bar to possessing or buying guns.