You prevent stress by not preventing stress. Figure out what's important to you (this will be different to anything you read, different to anything anybody will tell you), and focus on that. You chose to be a teacher so helping kids feel better is part of who you are it doesn't mean it will be easy but you'll be doing the right thing. Sometimes if you get fired up it just means you care. You shouldn't have to apologise for that or feel guilt, embrace it and suddenly that energy will be a good thing. Sweat isn't bad either do you think athletes worry about that? I sweat 12 hours a day sometimes hauling lumber and my skin doesn't care. It's normal. Humans would be extinct today if we never broke a sweat.
Health and all that is obviously good too, but it just gives you more energy and it's your choice what to do with it.