Before I begin, I'd like to state I am going to try and be as thorough as possible. Both so everyone offering help can know the full situation, and to ensure that I get accurate information.
Ok; I recently transferred to a new college, in a new city, and a new state. The method for accessing the internet is different from my prior University, and - although I'm confident in my current methods - I'd like to know for sure that my activities are as hidden as possible. Why? Because, although I live in the dorms, my dorm internet connection isn't currently working and they said it could be a month (!) until they get it fixed. So, the only internet I can get is through connecting to the Library's hotspot, where the rules are more strict and all that.
The set-up: I've my own laptop, but to access Wi-Fi one must log on with an assigned username & password. I've downloaded the TOR browser, set it up and it works fine (I get a different IP address and all that); but, will this be sufficient to keep my browsing private from the System Administrator? What if I opt to browse outside of encrypted mode?