Set up filters for any specific senders you feel are going to be the likely cause of stress. These filters should virtually hide the email from you, not even a visible label with an unread counter.
It's funny how, as a wise phrase I've heard before, "nothing is ever as good or as bad as it seems"
After a few weeks of whoever might have emailed you, but you didn't see it, or maybe they never emailed? But at least you can continue your life and still see messages that probably matter.
Email sucks in this way, it's hard to fully ignore it, but you can fully ignore certain senders - which I have absolutely had to do in the past.
Time + the above strategy will really help, I think.
-- Disclaimer, I work on 'better' email products.