First Time Asking for ADA Accommodations and I'm Scared

I recently started a new position at work (about 4 months ago) and it has been... not what I was led to believe. There's absolutely no coverage except for e which means my training has been cut short a bunch so I can cover places that I haven't been trained in yet. Plus extra hours. Denied time off. All sorts of fun.

Its gotten to the point where im so anxious about work I cant sleep. Last week a denied time off request tipped me into a hypomanic episode and I finally requested that I be moved down to 32 hours a week instead of 40 (still full time and with plenty of time to get my work done but with some breathing room.

Management said no. They said that a new hire would be starting next week and it would be improving how much is currently on my plate. For a lot of valid reasons I dont believe them (about conditions improving) and so I went to my therapist and asked her to write me an accommodations letter requesting the 32 hour work week as an ADA accommodation.

Ive never done this before and im so scared they'll just say no again even though they've given an insane amount of accommodations to others (its a favorites game around here). So ita not out of the realm of possibility that it'll work out but....

Has anyone else requested an accommodation for something that was previously denied when they asked informally? Any advice? Im floundering here.