Email affiliation for an undergraduate student with a complex university address
Use your university address, even if it is weird and complicated.  Nobody will hold an official bureaucratic policy of your university against you.

You may, however, wish to see if your university supports email aliases.  Many universities have an official "full" email address, but also a shorter and easier version.  Others allow you to activate your alumni account even while still a student, and you might then use that alternate (and persistent!) address.

Separately: do not hide your paper from your professor.  Assuming your professor is basically ethical, then either a) your professor should be an author and will explain why you should add them, or b) your professor should not be an author, in which case they'll celebrate you without asking to be added.