In the options, you can set LimeWire to use a specific port for incoming and outgoing connections. It's normally 6346. Remember to change both incoming and outgoing port.

It is possible that the network administrator at your school is blocking that specific port. In that case setting LimeWire to another port might help. However, chances are that they're blocking all ports except the ones needed for essential services like surfing the web. In that case, you need to access the internet from elsewhere in order to use LW.