Couple of ways to do it...
One way is to set up an anonymizing web proxy on your home computer, then browse to your home computer from school. That way your school computer only connects to your home computer, while your home computer goes to the forbidden sites and simply passes the info back to you along the permitted connection.
There are other anonymizing proxy servers out there, but many commercially available proxy servers like the one your school is using will automatically block known third party proxy servers. That's why using one on your home computer has a better chance of success.
There are risks of course... If you don't have your home computer secured well enough and install a proxy server, you might end up having your home computer attacked and taken over by hackers. So you'd get an A at the cost of your home computer and any other computers set up at home. That would sort of suck eh?
Another way that is more secure is to set up a secure peer to peer tunnel, again using an "allowed" port through your school proxy, to a computer somewhere on the internet (you could use your home computer). This would essentially be a VPN hookup from your school computer to your home. You pretty much log in to your home computer from school, and from then on it's the same as if you were using your home computer. Two problems with this... First, you might need to install some software on the school computer and that is usually a huge no-no (punishable by at the very least loss of computer privledges, possibly suspension, possibly even criminal charges). Second, whoever set up the proxy might be really talented and may have set it up to detect VPN and other tunneling efforts.
If you don't know what "tunneling" is, you lack some of the basic knowledge you need to pull off what you said you can do. In that case, you need to give up or try harder. Meaning you need to actually learn the nuts and bolts of networking, all of which you can easily do from home using freely available textbooks and how-to documents. But you'll need to put some effort into it.