I hope you find the answer to this question. I think you'll have to apply for disability rather than unemployment, but I'm no expert by any means. From what I've read, they do consider problems like agoraphobia and panic disorder to be legitimate disabilities now. I quit my job 6 years ago as I was in such a downward spiral that I found myself calling in sick several days a week. It turned out I was just a couple of weeks away from a full-on adrenal breakdown. At least I think that's what it was judging from all I've read up on it. I wasn't able to see a doctor because I no longer had medical coverage.
My point is that now that you've made this decision, be sure to get the answers you need. I procrastinated because I didn't want to be labeled as disabled. It seemed so permanent. I lived off my savings for a while, and now I'm basically living off my mother's generosity. The other day I got a letter from Social Security saying that because I've gone 6 years without working I no longer qualify for disability. I should have applied for it while I still had the option. I'm trying to see this in a positive light, that now I have to get better because I have no other choice. However, having no money and no insurance for medical care adds to my health anxiety (which is my main problem). Don't make my mistake. Get the information you need, and make an informed decision. If it's too much to think about now, perhaps a friend or family member can help you do the research necessary.
The ironic thing is, now in hindsight I can see that if I had held a different attitude I wouldn't have been so miserable at my job. Yeah, it was a lame job, but I think it was my negative state of mind that drove me into the ground.