Do this:
Log on to you University email account using Webmail. (a fancy name for a simple process of connecting using a browser).
Settings there including Out-of-office notification. and generally include an email address to always forward to. Change the settings there and every email should be forwarded to your <new email address>.
Having multiple email address in apple mail is not an issue. I have a habit of keeping my old email addresses, unless defunct, and manually notify senders to please respond to <new email address> in future.
You can also specify in your Mac email sender to ALWAYS send from a specific one of your email accounts, so that when readers click 'Reply', they will reply to your <new email address>.