I was trying to think of a profound answer, but equating "tease" with "vex" makes sense to me. I think Fanny was most upset that Edmund was morally compromising himself. That she might compromise herself morally didn't matter as much - especially when there might have been some justification for her to participate in gratitude to her cousin Tom's wishes even if it was against her better judgment. And she also had her own timidity to overcome which was not something for her to be proud of either. But she also now didn't have any defense herself. It was fortunately Mrs. Grant stepped in for Fanny, to save her now that Edmund was lost.