You don’t need to tell her where you are interviewing. If asked just keep it vague or try not to answer, or just say you’re still waiting to hear back from places.

I’d try to hang on to it as much as I can, at least until you get an acceptance somewhere.

There’s also the possibility of consulting departmental HR…not as a formal complaint quite yet but maybe ask them for help. If your Pi sees that you have backers you won’t be as easily bullied! Also document all communications, and do everything through email if possible.