Tor does encrypt data in multiple layers, so that Your cell provider / University network will only be able to track the traffic to the point it enters the Tor network. However, it is decrypted at the exit node so, unless the connection to the site you're connecting to is encrypted (i.e. over HTTPS or another secure protocol), that node may see data that identifies you.
Also, if you have ever used your browser/accounts to connect to the internet without going through Tor, it may be that cookies allow your connection to be traced back to you/your ISP.
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