I was in a similar position to you a couple of years ago. Burned out and quit my job, burned through my savings instead. After two months I felt no improvement and was beating myself up for being a failure, but after ten months I felt oddly re-energised, and ready to resume working.
I don't know what changed, I think it was just time taken to recover my mind. I wish you the best, it's a difficult state of mind to be in.