If you go here:
http://twitter.com/goodies you can find the code to add your Twitter feed to your website.\
Here is a site that lets you send tweets via email:
http://tweetymail.com/
You can also use apps like Tweetdeck to send/receive tweets, but if you can't access the twitter site, you probably cannot install an app like Tweetdeck on your schools computer.
Good luck and enjoy