I’m so sorry you have been carrying these feelings for such a long time. I’m sorry no one helped you back when you were small. It’s likely that your sister wasn’t rejecting you so much as trying to claim herself. I gather that she is more than a couple of years older than you. That means she was at a different developmental stage and working on separating from her younger self — a self that was represented by you. The new kid was let into the group because she was exotic to them. She didn’t remind those older girls that they had just emerged from being a younger kid.
I’m glad you understand that you probably magnify the “rejections” you experience. Chances are, you are super-sensitive to the possibility. The answer to your discomfort lies within yourself, not in getting people not to “reject” you. If your self-esteem were more secure, you wouldn’t be so concerned with what other people think.
You can’t make other people change but you can work on you. I suggest you stop focusing on what happened when you were little. Nothing can change that. Instead — work on the present. Find things to do that make you feel good about yourself. Get involved with community service projects that make a difference. Find activities where other people who share your values hang out and do positive things. Knowing you are a good person who does good things will help you believe in your own self-worth. Once that is secure, I think you’ll be much less likely to get into that jealous and angry place.
I wish you well.