If the storage space of your mailbox is full, no new emails can be received. To free up space, it can be useful to delete all emails at once.
Please use the webmail of your university on your laptop or PC. This way you will have a better overview of this irreversible action.
To find the webmail of your university, you can use Google to search for the name of your university and "webmail" and you will quickly find the right page.
If you don't seem to have freed up any space after deleting, check the recycle bin or trash folder. This must be emptied to have an effect.
Many universities use Outlook as their email service. You can find out how to delete all emails via the web view here: https://support.microsoft.com/en-us/office/delete-all-email-in-outlook-on-the-web-050de480-7908-4132-90f2-6de3a81f5e4b