You can cancel your Adobe account purchased independently at any time, although Adobe will not reimburse you for any unused time on your contract. Once you set up your new account on the university's Adobe plan, you can start moving your data from your previous Adobe ID to your university account. (Your university account is referred to as an Enterprise/Federated ID account in the Adobe instructions.) Adobe instruction for manually transferring your assets is available here.
Your files remain with your previous Adobe ID for 90 days; after that time the data availability is reduced to 2GB.