Honestly sweetie I think you should just give your sister some time and space. It'll give her time to cool off, and then approach her and just hash it out (aka talk calmly LOL). Make sure she understands the truth, and if she refuses to listen then maybe you shouldn't be friends anymore. True, you'll always be sisters, but don't fake friendship just because of that. (Does that make sense? I don't want to sound harsh, but something like that happened to me.
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Either way I hope this thing works out.