I think you have to decide what is more important to you – your friendship with this woman or your privacy. I suspect that you can’t have both. Do you fear that if you break off the friendship she will get revenge by telling everyone she can about your status? I think this is actually unlikely. From the way that you describe her, it sounds as if she is indiscreet about you mainly when in your presence. I would be inclined to celebrate the fact that “she now refuses to speak to you” – friends like that you do not need.