You are correct. However, it's possible to get antidepressants under health insurance without them specifically being separated into a mental health category. Depends on the insurance, as well as the doctor. Potentially something OP could see if possible.
Further, my prescription is about to run out soon, and I've found that I can hypothetically get 100 of my meds (generic) for about $35, using one of those Rx discount cards, ie, something like pic related. They do work if your pharmacy accepts them, so call ahead.
I've not tried SSRI, but have heard it works for some people and not for others. As you said, the situation is important, as well at the individual's reaction.