Help with my annoying sister!?

RIGHT NOW before she does anything else bad to you sit down and talk to your mom, say "Mom, *Sisters name here* is faking a lot of the things that are bad that I have never done." Then honestly tell her the bad things that you have done in the last say, month. One way to to get back at her is show your mom her the receipt from the store you bought it. Sorry, I don't have brilliant schemes but, next time she does something awful argue a bit then run to your room crying and lock your door. Use makeup to make it look like you have been crying and hide a cheap recorder bug in your hand then say "*Sisters name here* why do you hate me?" to start a convo, in the convo say stuff like "Well, why did you frame *Best friend in the entire world's name here* and get him banned from the house?" I think that this will get her to say something like "Well, he was annoying." which is like admitting it. Then show the bug to your mom. Sorry if this doesn't work.