I concur with the prior two comments, pretty much wholeheartedly. Not only is there no guarantee that your sister will be admitted wherever you are, even the most warm and fuzzy (but otherwise non-therapeutic) schools are places I would absolutely not send a child with the conditions you describe (and frankly, in the case of many schools, they will not relish the idea of admitting a student with an eating disorder already on the books).
Also, to your response, I still don’t understand the basic premise. You say “lack of consumption of food has basically consumed my sisters life” and then say that therefore she’ll go where you go. Why? Do you provide care or oversight? Genuinely asking. If you do, this will almost certainly not be something you can continue to do even if you somehow wind up at the same boarding school, which isn’t likely all things considered.
Not trying to discourage you. In fact, I’m trying to encourage you to focus on you. Not “selfishly,” but recognizing that your sister’s path is her own, cannot be planned for or guaranteed in advance, and may very well lie along a (very) different path than your own.
What’s the best situation for you? What’s the best fit for you? That’s the path to pursue.