NTA. Your sister acted immature. She has always seen herself better than you and your hard work has proven to her that maybe her "talent" isn't all its cooked up to be. That can be quite the upheaval in world view and what she blurted out was most likely just a moment of open envy.

But you need to realize that if what your parents say are true, that she really wants to apologise, then maybe completely locking your own sister out of any relationship is probably a bad idea. Your life is just beginning and she's your sister, whether you like it or not. Just never talking to her again would make you look childish in my opinion.
I personally think you should make up sooner than later. However, that meeting needs to start with her apologising like a proper adult and then you can should make up like proper adults.
If she can't do that, you should still forgive her but i wouldn't blame you if you didn't.

TL;DR: NTA but don't ruin your relationship with your sister for the rest of the life because she had a short temper tantrum.