Thanks for the info from everyone so far.
The big problem is that I still live with and am dependent upon my parents. I'm on the autism spectrum and struggle with a lot of mental health issues, so it took me six years to get through college. I finally just now graduated, so I don't have a job yet; I had to quit my most recent internship/part-time job because my depression got so bad.
We're by no means poor, and I'm sure we could make it work by being more thrifty than we currently have to be. So it's more about justifying the costs to my parents if we would have to pay out of pocket. They've accepted me well, but they're not so keen on forking out more money, especially since I'm so dependent on them for everything else.
I've tried to explain to them that it's just as vital to my health as my antidepressants, therapy appointments, etc., but they haven't seemed to understand that.
sighI have considered appealing the company. I've interned there several times and have had pretty good experiences; I even worked with the HR employee who deals with health benefits. I'm just not sure where to start. If anyone who has appealed their company is reading this, could you comment on how you went about that?
Wow, I apologize for the long post. I can tell I'm stressed about this because last night I had a semi-realistic dream about successfully appealing the company and coming out to my previous coworkers. Who knows, maybe I'm psychic?!

Here's hoping, anyway.