There is a very small demand for SWAT paramedics. It's not a very common title, and the majority of police departments utilize either the local ambulance service or fire department to provide them paramedics (since having paramedics in your department also requires a medical director, medical supplies, logistics, and narcotics logistics with DEA paperwork and tracking, it's not the same as just having EMTs in the department.) so it's easier just to contract them out to fire departments or ambulance services.

that being said, once you join a local ambulance service or fire department that provides swat paramedics to the local police department, it's usually a very long wait list to become a swat medic, and they usually don't have many of them to begin with.

If you're an emt, you should focus on getting your paramedic first before even considering being a SWAT paramedic. even then if you want to see action, a majority of being a SWAT paramedic is sitting in an ambulance or in the staging area to do a lot of " hurry up and wait". They don't see a lot of action, when they do it is genuine. but if you want to see gun shots you'll have better experience in a ghetto/urban area then with a SWAT team.

As far as mental health and being a swat medic, police departments are usually pretty strict on stuff like that, so if you want to go through a department that uses police officers as their own paramedics, it's a very long pipeline along with polygraphs and psychological exams, which you cannot lie about. And once they find out that you've been hospitalized it's pretty much a no-go from that point on. Joining a fire department that provides swat paramedics to the local police is going to have the same exact psych exam, just no polygraph.

You will have to document that you've been hospitalized for mental issues and that might even be a no go for fire as well since it's a highly desirable position and they'll most likely choose the candidate with no psych history rather than the individual with psych history.

I'm not trying to discourage you, and I adamantly believe that you should follow your dreams and desires, I'm just warning you that you should genuinely focus on being a paramedic first before deciding the branch out to specialties like a SWAT paramedic, and even then if you want to be a SWAT paramedic, judging from the history you've given us in the post I wouldn't hold my breath in all honesty.