I believe that AccuRadio might work. It's free, and you can get an account by using other social media, like Twitter.
What are some unblocked music sites in school?
www.convert2mp3.net
I'd recommend trying Grooveshark, seems to work for me almost anywhere.
You can also try using a service like https://www.hidemyass.com/ - it acts as a VPN (hiding your ip address), and sometimes works to get around firewalls.
If you have access to YouTube, then they've also recently beefed up their music offering.
You can also listen to music direct from the artists through sites like http://www.reverbnation.com/
Finally, some musicians also host music on their own sites. One of my favorite bands does luckily!