Visit wadcmd.com to play directly in your browser. This site allows you to upload your own .wad game files (like doom.wad or doom2.wad ) which you can find in various GitHub repositories.
Some schools allow access to a limited version of the Google Play Store . how to play doom on school chromebook
If your school has blocked common gaming sites, you may need to use a proxy or "unblocker" to access them. Visit wadcmd