If you are running transmission in the background,
1. At best you are clogging up internet that they have allocated for everyone. They probably don’t buy a massive amount of bandwidth so everyone can download/upload torrents at the same time.
2. At worst you are opening up the school to charges of copyright infringement by the RIAA and MPAA (I’m assuming you aren’t downloading GPLed content). These organizations could technically sue the school for actions you have taken. Every network is responsible for what it’s users do on that network.
That being said, you have a couple choices. You can spoof your mac address (change it to something else). There are tons of programs that do this for all operating systems. You could also buy an external WIFI dongle like johnpowell has suggested above. The new device will have a completely different MAC address then your old wireless card.
Or you could go talk to the guy and get yourself unbanned. This is by far the easiest thing to do.
*a quick note: At my college we had to turn in our mac addresses before we could get on the network. You had to specifically be allowed to use the network before you could get on it. If you had to turn in your MAC address to use the system, the only thing that will work is talking to the system administrator. No matter what the case, if he found out you were trying to work around the legitimate channels, he would possibly get angry with you.