A key thing that is very important to your recovery from a burnout is the difference between two words: healing and curing. The last word suggest there is a 'cure' to an illness or physical ailment called burnout. But there isn't even a clinical definition yet that doctors can agree on! So my advise is simple: don't see yourself as ill or otherwise damaged. See yourself as someone who just needs rest after a long period of stress. You simply need to heal.
Imagine yourself training in a gym. You're lifting weights and running on treadmills in a 'work hard, play hard' fashion. Afterwards your body needs to rest and recover right? Give it enough time and you come out stronger than you were before you had entered that gym. You've healed and you've become fitter.
Now imagine that same gym but instead of taking enough time to rest after your workout, you plunge in again. And instead of giving that workout time to do its work in your body, you go in again. And again, and again, and again. You're catching my drift right? That's what your burnout is: for too long, with too high expectations, you've gone without proper rest.
What I'm saying is this: your body and mind have everything they need to recover! All they need is time and rest. They will always work it out and they will always heal. You are not sick or otherwise broken. What you are is in need of rest and recovery. And the beauty is that however much you are hurting right now, you will come out much, much stronger. Just like that workout makes you fitter, you will be able to shed a lot of excess weight.
I know you feel terrible about it. But being a couch potato is nothing to worry about, it's the only right thing to do.
So get on it now. You deserve it.
Take it easy as always.