> "be your own therapist" That's impossible. It's like being your own dentist when you have problems in your teeth.
Sometimes it's possible, and sometimes it's not.
To respond to your analogy, I would equate "checking in" with your mental state with brushing your teeth.
No, you can't perform a root canal on yourself, just like you can't bring yourself out of spiraling depression or a mental disorder -- you can, however, do some "preventive maintenance," and take care of your mental state. Seek a professional if/when you need one.
"Burnout" is a nebulous state. Some people are burned out when they've had a hard week, and others are in an intense state of panic/depression. I think these should be treated (or self-treated) accordingly.
Actually I've found that reading certain books and watching certain movies makes me very introspective, and I can diagnose a lot of my own problems by journaling.