The only thing you can control is how you react and feel about things. Your sister has the right, as you know, to pursue whatever interests she likes. The fact that she copies so much of what you do can be seen as a little flattering. But since you feel the way you do, I'd suggest speaking to a therapist about it.
Another suggestion is to not spend that much time with her so that you don't get annoyed by this so much.
It sounds like you feel your parents give her special attention and treatment. Do you think that's really true? Your therapist can help with this, too.
It really is worth seeing someone - no one should feel the way you do and it's likely never going to stop unless you get some clarity and insight or, at the very least, some understanding and coping mechanisms.
I think many would feel the way you do and one way to address it is to make jokes, "Wow, you're copying me again
?? What would you be doing if you didn't have someone to copy?" along those lines. Maybe she just thinks you have great ideas.
But I certainly do get your frustration!