First off, thank you all for your generous advice. This forum has really exceeded my expectations. You have shown care and concern for me, the students, and the discipline with these thoughtful suggestions.
I have done some research into the institutional guidelines here at my institution. I certainly have veered into murky territory. I should clarify that by "romantic" I didn't mean professions of desire or anything related to love. Our conversations were of the kind of intimate conversation that could occur between good friends. What worried me was that the subject of our post-class future did come up once. I should have said I could not comment. Instead, I advised we "play it by ear" once that time had come.
I am following Rising Star and other's advice to cease communication. I am sending a final message informing the student of my intentions and asking her if she will still be comfortable studying with me. In no way do I give the impression anything should be swept aside. Sigaba, I've learned much from this experience. You were right to shame me for this behavior. I wish every institution was as committed to creating a culture where everyone was aware of these necessary boundaries. I don't mean to excuse myself, but in this part of the country, many of us don't always know how to proceed when situations like this arise, especially those of us not wholly familiar with academic norms and expectations.