Well now you know something about her that you didn't know before. I would feel uncomfortable about it too. There is a sense of confidentiality in asking questions from an authority figure, like a teacher and facebook blurs the boundary of what is public vs. what is private. You had every right to expect your conversation to be private.

I think it is a highly personal matter how to deal with it. It would partly depend on how well or poorly she might respond to any form of criticism and whether you want to take that on while you are taking a class from her.