I don't know how to say sorry to my sister?

It all began Saturday when we decided to go to the movies. While we were getting ready, she took my gray cardigan off the hanger and asked to borrow it. Well, that sort of annoyed me because it was like she expected me to automatically say yes. She does this all the time, borrow my cardigans I mean. I own a lot of them, and most of them are loose, because I like them bigger than my size, and they happen to fit her, unlike my other clothes. You see we're different sizes, I'm a small and she's a large. Anyway, I don't want to be selfish, so I usually let her borrow them. But this night I was particularly annoyed for some reason. Anyway, we depart to the movies, and when we're driving home, she slips in, "Oh, by the way, I'm meeting my friend _____ now." And that kind of bothered me, the fact that she just said that then, rather than prior to the film, because I was expecting to hang out with her the rest of the night. So we get home, and she's touching up in the mirror, and I go to grab something from the bathroom, and for some odd reason, I still don't quite know how this slipped out of my mouth, I guess my impulses got the better of me, but I said, "Oh, are you going to wear my cardigan?" And she said the affirmative. And I said, "I don't want you to wear it." And she basically, freaked out from that point. She was yelling and screaming at me saying I was a selfish, and a bad sister and friend, and countless expletives I won't dare mention. It still kind of hurts to recount that night. But anyway, we haven't spoken since then. And we're both on college winter break, so we're in the family house, not speaking one word to each other. And it sucks, and I just really have to apologize so we can start talking again. But I'm not sure how to bring about it, I mean, I'm afraid my apologies won't be good enough, and she'll still refuse to speak to me, or even forgive me. I'm a little scared to be honest. I need help. Any suggestions? Thanks for any replies in advance, I really appreciate your input. I just want my sister back.