Cultivate serenity. Try setting office email hours for a week. Decide on specific times of day to check and respond to your email. For example, 10 am, 1 pm, and 4 pm. Add a note about those times in your email signature along with a phone number in case of an emergency (it’s amazing what is no longer an emergency when someone has to pick up the phone and call you). Then, set alarms to remind you to check your email.
If you are uncomfortable giving out your real phone number, consider getting a Google voice number (or something similar). It’s free and you’ll have a number to give out when you want someone to reach you but don’t want to give them your personal number.