I am sorry for a probably uninvited comparison — I am not implying that my situation is harder, and I know that burnout is a serious shit. It takes months to recover.
Some things to consider:
1) Even if you feel like a failure, you are not. You are a success. Our feelings are not a reliable indicator of personal value, especially after burning out.
2) Try to do something where you can feel small improvements every few days, with enough runway before productivity plateau. Running, meditation, skateboarding, playing guitar, rock climbing — whatever looks the most interesting to you, and looks easy enough (it's important). Regularly feeling improvements in any activity is the best therapy I know.