First let me just say that hospitals block certain sites for a reason. I myself am admitted into hospital frequenty and some sites are also blocked there. Luckily for me there is no limited internet connection, I can go on it when ever I want, although the connection is not the best.
You may want to use www.poxyproxy.com which is always a life saver for me when I stay in hospital. This should work for you, there is always uncertainty though as my hostpital blocks most proxy sites too, luckily for me so far it has not been noticed.