I am very glad you wrote. You are correct that this isn’t normal sibling rivalry. Without talking to your sister, I don’t know what is going on for her but I have a couple of ideas for you to think about:
You said that your sister has been picked on by your older siblings. It may be that she doesn’t trust you even though you are nice to her. She may think it’s only a matter of time before you pick on her too. She can’t stand the anxiety of waiting for you to bully her too. She therefore provokes you until you confirm her worst fears that you are no different from the others.
It may also be that she has no idea how to be in a friendly relationship with a sibling. She provokes you because to her fighting is “normal.” Fighting does keep people connected with each other, even though it is an unhappy connection.
You are right that she doesn’t really need a fight. She needs help. But until she gets some help, the person who can change things, at least a little, is you.
You can’t change how your sister treats you. But you can do better at declining the invitations to fight. Remember: When you flip out, you are inadvertently showing her that her manipulations work. Instead of fighting, find a few phrases to use to respond like “I’m sorry you feel that way” or “I love you too much to fight” and then quietly and calmly LEAVE the situation. You can go to another room. If she follows you, go for a walk. You can go to the library or a friend’s house. The exception to this is if she ever escalates to physically hurting you. Then do involve a parent immediately. Even then, keep as calm as you can. Stress your concerns about her, not your anger. Do tell her how much it means to you to have a sister to talk to whenever she is behaving decently.
Yes, this will be hard. Yes, it isn’t fair that you should have to put up with your sister’s abuse. Things aren’t always fair in families. I hope you can look at this as an exercise in teaching yourself how to stay centered in spite of what others say.
I hope your parents will reconsider their attitude toward therapy. You are 18. You can do the groundwork by looking for a therapist who specializes in family work. School guidance counselors often know where teens can get free or low cost therapy. Once you identify a therapist, you can give that information to your parents and see whether there is insurance to cover it.
If no one else in the family will go to therapy, please consider going yourself. You deserve to have the ongoing advice and support of a therapist.
I wish you well.