Normally I would recommend OpenDNS for stuff like this, but since he's probably monitoring more than just DNS requests that would not solve anything.
If you can get a friend to give you an account on a pc and run open ssh server, You could set up an ssh tunnel where everything is encrypted, what you would need to do is use something like Putty to set up the tunnel, and then set your proxy options in your browser.
This leaves DNS requests in plaintext though, but in firefox atleast you can send the DNS requests through the tunnel therefore encrypting them (Once you have your proxy set nagivate to about
:config and type dns in the filter box, then from there make network.proxy.socks.remote_dns TRUE)
Hopefully this answers your question and i'll include a few links for info.
Ssh tunnel - Wikipedia, the free encyclopedia
SSH Tunnelling (Port Forwarding)
Tunneling PuTTY through a Firewall at Your Company or School
If you have any more questions, feel free to ask.
