It is well known that a college that you are attending has access to your browsing history. Does Tor prevent this injustice?
Assuming the computer is yours, then no, they can't access your browsing history. They can know you are using Tor though.
No. All they can see are outgoing requests to the Tor network. These can be blocked though, so be warned. Use multiple no-log VPN's that change every few hours for the best result.