Its likely that you have given up all rights to private use of your schools network as part of its conditions of use. This certainly applies in most privately owned networks, including the one where I work. In my position as the IT Security Advisor at my office Id be... upset... if I found someone trying to secretly tunnel data out of my network. "Get a person fired" upset. Just so you know that what you're doing may bite you in the ass.
If the network administrators know what they are doing, you will never be able to hide completely. Decent encryption may hide the details of what you are doing, but it wont hide the fact that you are doing something - the encrypted channel can still be noticed, even if the contents of the transmission cannot, and this may be enough on its own to arouse suspicion.
Changing port numbers wont actually change the details of how a protocol communicates, though it may fool some analysis tools that attempt to match protocols based on port number. Depending on how monitoring is done, this may actually make traffic more visible (seeing significant outbound traffic on port 56 would make me really suspicious, traffic on port 22 less so - dependant on whats normal for the network of course). In addition, if proper outbound packet filtering is done the question of changing ports may be moot anyhow.
You're definitely overcomplicating things. There is one really obvious and simple means of establishing an encrypted outbound tunnel which is very likely to be working in your chosen environment, and which would result in your traffic getting lost in the noise of many other similar types of connection.