Answer the message! Start the task! Get it done now! Much of our response to urgent requests is perceived, but we're generally the ones who assume the urgency. Sometimes we're right. Often we're wrong. Reduce your stress by greeting every task with one question: How urgent is this really?
Realize that if something is truly urgent and needs to be dealt with in the next hour or two, an email probably isn't someone's first choice to reach you. A text might be. Set aside several times during the day in which you'll open your phone and check on things. Talk to superiors, people who report to you, family members, and close friends. Set up a way for them to reach you promptly when necessary, explaining that you're trying to bring your communications under control.