Your First Class Medical is your first hurdle.
You can try and spin it every which way but you were released from the military for psych reasons. That’s a big liability for a future employer, especially the top tier airlines as there’s a lot of money to be made in lawsuits.
Even knowing a couple of airlines will hire you doesn’t mean you’ll have a satisfying career if you can’t move up.
Yes, there are times that airlines will hire with DUI’s, arrests, felonies and what not but that stops the next cycle comes around.
Get your Medical, get your Private and see if this is really something you’d want to pursue.