Hm-m-m-m... well... I've never been self-employed exactly. But I was a more-or-less professional person when I was working & I think there are similarities. (By the way I was a vocational rehabilitation counselor.)

Personally, I would think one of the main issues is going to be that, as a self-employed person, your success (or lack thereof) is all on you. You either do it or you fail. And there's probably no one to share your success or failure with... little or perhaps no support system. Isolation can be a big issue in self employment.
I also noted that you wrote you could probably not participate 8 hours a day 5 days a week. I think most self-employed people find that they're spending more hours per week working ... not less than would a person who works for someone else. Not only do you have to do whatever the work is that you're involved with, but you also have to keep track of the finances, & do things such as send out the billings for your services, deal with late or non-payers, handle complaints, order & maintain supplies & whatever else comes up.
I know there are other members here on PC who are self-employed. It would be great if some of them would reply to your post. They would have first-hand experiences to share. I don't know what skills you have that you think you might be able to offer as a self-employed person. Obviously you have to have some skill-set that is in sufficient demand that other individuals or companies will want to do business with you.
I would certainly not want to say that a person with mental illness can't be self-employed. However my personal thinking would be that if you feel you could not handle being in someone else's employ, I find it difficult to imagine you would be likely to find success as a self-employed person.

But, then again, stranger things have happened I suppose. To some extent, it's your own level of determination that will make the difference!