I'm not a resident down there, but from what you've quoted of the law & explained of your situation it doesn't look like you're prohibited.
Also bear in mind that your private health records are just that - private. Without your permission, nobody including the gov't can get at them.
The reason they can learn of involuntary commitments, or being adjudicated mentally incompetent, is because those are court records & although usually not public they are available to the gov't.
It's sad that there's prejudice against brain disorders that doesn't exist w/r/t other diseases. It's worse when people consider 2A rights.
(But nobody suggests that someone with, say, schizophrenia should be prohibited from voting, or associating with friends, or worshipping, or having a lawyer present when being quesitoned.)
Too many people, some who should know better, think that any brain disease is a prohibiting factor, when really it's only the ones that are most serious.
If laws were practical, people with epilepsy or neuro / muscular* conditions wouldn't be allowed to carry. If they can't control their body, how can they safely control a gun? That's dangerous.
* that's 2 separate conditions, not the mis-writing of neuromuscular