Is "The girl who's bag is red is my friend" correct?

Why

Sakshi's mix-up is one of the most common in English, and for a good reason — "who's" and "whose" sound completely identical when spoken aloud, so there's no audible clue to tell them apart, only spelling. "Who's", with the apostrophe, is always a short form of "who is" or "who has" — "Who's coming to the party?" means "Who IS coming". "Whose", without an apostrophe, is the possessive form, showing that something belongs to someone — exactly the job needed here, since the sentence means "the girl, HER bag is red", a possession, not "the girl IS bag is red", which makes no sense at all. Test: mentally expand "who's" back into its full form and check if it still makes sense — "the girl who IS bag is red" is clearly wrong, which proves "who's" was the wrong choice and the possessive "whose" was needed instead. Her friend is right: "whose" shows possession (whose bag), while "who's" is only ever short for "who is" or "who has" — the sentence needs "whose".