["My friend would not stop whistling even though she knows I can't stand it.", 'Did you ask her to kindly stop?', "Yes but she wouldn't. I was so irritated by it."]
She may not be the best choice of a friend if she likes annoying you so much.  Maybe try distancing yourself from her for a while.
My friend would not stop whistling even though she knows I can't stand it. I was so irritated by it.