How do I restore my phone on a Chrome book that is the schools?

You cannot use a Chromebook to restore. The device needs to support iTunes, Chromebooks run ChromeOS which is a web only operating system.

Might be able to backup/restore using iCloud Backup on the linked Apple ID.

How to back up your iPhone, iPad, and iPod touch - Apple Support

Contact your schools support, they own the computer and would be responsible for it's configuration.