There are a number of ways to install Linux on a thumb drive so that it can run directly without accessing the system discs or files. For example, Ubuntu will allow you to install it on a thumb drive, and if the drive is 4GB or bigger, it will also allow you to allocate some of that space for writable data storage. There is also a tool call Unetbootin which can take just about any distribution ISO image and turn it into a live USB drive, just like a live CD/DVD. You can get Unetbootin here: http://unetbootin.sourceforge.net/
Just remember to check with the school about using the system this way. If you make your case, they should allow it, but remember that a live USB distribution can also install itself on the system hard drive if you want to, which would not be a "good thing"... :-)
