If you keep trying to check your school email but it keeps auto-logging you into your personal email, or if you have a computer that has multiple users all with Google Mail accounts, then these short steps are for you.
While logged into your email, click on your email address or picture in the top right of your browser. In the small window that appears, click on Add Account. There, you can log into any other Google Mail account that you want. If you return to this small window, you will see your added accounts for easy switching.