Toxic colleague talks about me to Professors
A campus is a complex social environment that not everyone can adapt to, which is why most campuses have a free, confidential consultation office regarding harassment and personal issues. I'd recommend discussing this with that office before trying to engage with this troublesome student directly.

It sounds like you have gone out of your way to avoid confronting this student, and you don't want professors to know about your negative feelings towards her. When you consult a third party, there is no need to cover up such details. Let the campus staff specifically know that


This person was making you feel uncomfortable.
You tried your best to avoid conflict by disengaging with her.
She is now complaining about you to professors, even though you are no longer communicating with her.


The professors apparently don't understand the full story with this student. It is wrong for them to ask you to confront her directly.