It's her life and her choice. My brother didn't want to hear it for years. He went to a psychiatrist 2 years ago for something unrelated and got diagnosed. He had to do it on his own for his own reasons.
You can't force people to do things. I understand you're trying to help and you think you're helping but from someone who did the same thing, you're not. You're pushing her to actively avoid it.
How to you present your autism to her? Is it just the things you struggle with? Is it just how you're different? Is it just negative? How about what you tell her you see in her? Are you only pointing out the negative traits like you are in your post? Or are you also pointing out the things that can make autism alright? "Hey sis, really cool drawing you did. I noticed art seems to be a special interest for you. I'm reallyv happy you have a hobby you enjoy so much!"
Now also ask yourself, why? Why does this matter so much to you? Why are you so upset she won't admit it? Is it really about her? Or is it about you? (I don't know the answer here, that's yours to think about)