you were not remotely rude.
I agree thst you need to speak to your boss again.
Be explicit.
"I spoke to you in cofidence. Jane not only evesdropped on that private conversation, which is not OK, she then made it public, which was totally inappropriate, and she has continued to speak about this after I have repeatedly told her I do not want to discuss my private affairs with her, or in public.
I feel that it was very obvious from the outset that I was not sharing that information with anyone other than you, and that even if she inadvertently heard part of our conversation, she had no excuse for repeating or referring to it.
Her refusal to respect my privacy, or to respect my repeated requests to her not to talk about this have been ignored. I feel that she is bullying and harassing me. I don;t know how I can make it any clearer to her how totally inappropriate her behviour is, so I am asking you, as our Boss, to make it clear to her"
Be prepared to proivide a chronology setting out all of the incidents, hen they happened, and your response (e.g. your requests to not talk about this issue)
If Boss brings up the 'she has your interests at heart then a response such as
"No, she hasn't. If she had my interests at heart she would respect my privacy, and my personal choice not to discuss this issue publicly. She knows I dio not want her input but is ignoring that."
If your Boss won;t do anythign, consider taking it higher up the chain of command (if there is one).
Do you have any more sympathetic co-workers who might be willing to back yuou up?
eg
Jane "you should ..."
You "I don;t want to discuss this, it's a private matter"
jane "but I want to help, you..."
SCW "Jane, give it a rest. Hollyandra said she doesn't need your advice."
jane "But if she.."
SCW "She said no. Stop bullying the poor woman. holly, can you help me with this workrelated thing?"
Better still if more than one of your co-workers is willing to back you up.
Good Luck.