It was wise to withhold your email address as you're likely to cop many irrational, denigrating responses.

Firstly, whatever you decide to do, be very mindful of the long-term damage that will occur to the student's reputation / status if your relationship becomes public - now or when she becomes your student.

Chinese university classmates tend to stay in contact for many years after graduating and call upon each other for favors from time-to-time. Your girlfriend may permanently lose both mianzi (face) and guangxi (relationship).

Given that you are already in a relationship with the student, I'd imagine that things would be much more awkward in the classroom if you end the relationship now, than if you preserved the relationship.

If you want to end the relationship now then you really need to leave the university now.

If you choose to preserve the relationship, stress to your girlfriend the need for extra vigilance in maintaining secrecy and explain to her that you will have to treat her equally, if not indifferently, when she is in your class.

Only you can judge if she is mature enough to handle the changed circumstances.