Not sure if this still works or not because Google has been cracking down on Youtube recently. But You could always use a video downloader to get the video to get it onto a flash drive.
Other more elaborate options such as a smartphone with Mini HDMI or MHL ports could easily hook to school computers (provided they had the right ports (HDMI)) From there the phone then becomes a projector of sorts as it then has a secondary screen
If your computer at school doesn't have HDMI in then you could very well bring your own laptop/computer to do that.
Hope this works.
- Andrew