dont get a router.
Get a wireless access point - You'll only be able to use 1 device at a time on the wifi but it'll be better than nothing and whatever device you use will still get a IP from the DHCP servers in your school.
If you use a router then you'll have to setup things like gatways and DNS servers and yout school's IT tech dept will know you have done this.
It makes sense. You are sure that they will be able to track if I had attached a router?