I am exactly in the same place (burnout) and here are a few things that have started to help me
1. Daily Yoga practice. (One session in morning and another one in evening. I generally do Yin Yoga in the evenings and it seems to help release a lot of stress). You can find lot of good Yin yoga videos on Youtube.
2. Write a Journal. Try to figure out your deepest motivations. Why did you act in ways that lead to burnout. Try to write about how you can bring back balance.
3. Have a balanced work schedule.
Also, don't forget.. "A job is just a job and it does not define you. You always have a choice"
May be you put a lot more stress to finish up things before you leave on vacation.
And that extra stress causes a decrease in immunity leading to sickness.
2. To let go off the need to constantly improve something or to constantly chase something.