I need this answered.

She might be. But it could be something else too. Something just as bad, like an intestinal worm. Anyway, あなた should tell your parents that you're worried about your sister. They'll know what to do. And don't feel like you're betraying her または something like that, because this is serious, she might even thank あなた some day.
Hope everything is going to be okay :)

Maybe あなた don't need this answer any more, but I'm still answering.
I'm not sure whether it is anorexia, but it sounds like that. Anorexia is もっと見る of a mental state when the person feels that any 食 going inside their body will make them fat, and like that. It's best to take counselling and guidance from a dietitian on how to increase the consumption of 食 in your sisters diet.