Hmm, well I see two possibilities
Believer, speaking as an outsider (non-muslim), logically speaking, I see 2 possibilities for your difficulties with your sister:
1. Your religion is, in fact, correct, and your sister will pay in the afterlife for her actions now in being happy, in which case, you are right to be concerned about her.
2. Your religion is not correct, in which case, your sister will not automatically suffer in the afterlife for the mere fact that she is happy now, if she is not actually hurting anyone. If that is the case, your feelings for her are possibly motivated by jealousy/ sour grapes, you yourself have chosen not to pursue your own happiness, so don't want anyone else to either.
At any rate, it's impossible for one person to save or damn another person's soul without their consent. You can physically lock up a murderer to prevent him from carrying out the action of killing other people, but you cannot save his soul and force him to be sorry for his actions in his heart. Since your sister isn't killing people, merely making them emotionally uncomfortable, it would be inappropriate to lock her up or otherwise force her to stop. You should try to accept and love your sister for what she is, not compare her to yourself in pride, or worry about your own reputation, if other people do not like what your sister does. You should worry what God thinks of you personally, due to how you have lived your own life, not what other people think of you because of what your sister may or may not have done.
I had similiar difficulties with my own sister, when I went to school, I was often beat up, and had worse things done to me, because I did not act in the usual way expected in my school. My own sister one day said that it was harder on her, merely to be the sister of someone like me, who was always beat up, even though she was never beat up, because other people did not think well of her for being the sister of someone so strange. And, according to her, her not being thought well of was harder on her, then it was on me, to actually be beaten up many times, because she said she had feelings and I did not!
Well, I do have feelings. They may not be feelings she understands, but I feel many things very strongly. Not all people are the same. There are people who are born color blind, and they cannot see colors, but there are some things that colorblind people can see that you cannot. It may be that God wishes for some people to be colorblind, to see things that other people cannot and tell everyone else about them. Perhaps there are things you do not know about your sister. I heard once of a man, everyone thought he was a very bad man, sometimes he spoke harshly to people and other times he drank a lot, but after he died, it was found out that for most of his life, he had secretly given much money to the poorer people in his town.