It certainly isn't your fault, but it's not fair she is taking it out on you either. It reminds me of my family. My husband was married and had 3 kids, got divorced and we married a few years later and had 2 kids. Well the very oldest was used to getting all the attention while growing up but when my daughter was born, all of sudden she became very jealous because my daughter get a full time dad, and not a very other weekend visitation type of dad. She is in her 30's now, and still can't get past it. She claims my husband loves his new kids more than here. Other than therapy, I am not sure what can help because she just only sees herself as a victim in this.
How old is your sister, as this seems really immature for an adult ?
But I have seen my mother in law and her siblings in this type of fighting, and they are in their 80's. lol Good luck, I hope it can change for you. Have you tried talking to her about why she has to take it out on you? It wasn't your fault.