Hi, Callista!
Thanks so much for stopping by the Apple Support Communities. It sounds as though you received an email that took you to a site asking you to sign in with your university login information. Face ID popped up, but before signing in, you exited out of the site as it was suspicious, and we understand you're concerned your information may be compromised. We'd be happy to help!
While we cannot say for certain whether any of your credentials were indeed compromised, we would suggest changing your login password for the account in question just to be safe. If your Apple ID was involved, you can follow If you think your Apple ID has been compromised - Apple Support to get information on changing your password, and other available security options to protect your account and data.
Best!