The thing my family has done, that helps the most, is live a happy life, despite my problems. I would tell my wife and kids in desperation, "Just be happy without me, show me how it is done." If they focused in on me and became emotional a desperate with me, it just fed my insanity. Then, I felt guilty that not only am I crazy, but I'm driving those who live me crazy too.
Like Bubulous said, write down her moods, you don't have to talk about it. My wife did that and she told me years later. I have used those journals she kept to see my patterns and cycles, once I was clear enough to actually use that information. Try to be happy as an individual, don't ignore her feelings, but focusing on you being happy might help her do the same and see in her sister what she wants. Don't give up, but don't give it more attention than it needs.
If she's not hurting anyone physically, or herself, then she is okay. She wants you to be happy as much as you want her to be happy, so try to give her that. Try not to let her see you suffer because of her, let her see you overcoming your obsession with healing her, and live the life you want for her.
Ahmad you see to be very interested in your sister's mental health. I am glas she has someone like you in her life.
That being said I would not worry as much as you do about her diagnosis. For one it is her personal journey and it is for her to deal with. You do not need to worry about her medication or try to diagnose or fix her.
Self-talk is something everyone does. Some people like do do it out loud because it helps them concentrate, come people keep it in their heads. If you want to help her try to get her on here or help her to journal and keep track of her mood through a daily inventory of herself.