There are a lot of prospective applicants who live with chronic conditions and illnesses. Suffering from an illness, in and of itself, does not present an “interesting case” for admissions to selective universities.
Aside from the general mapping to “Ivy League” with no other discernible hints of seeking actual fit, the second most concerning part of your original post is this:
That at least implies that you have no resume of qualifications with which to recommend yourself. “I suffer from fibromyalgia” is not a qualification. So, how did you even find fit? Why would “Ivy League” universities find “fit” in you? What talents, skills, qualifications, special or unique abilities, etc… can you offer to highly selective universities as an international applicant.
If you get shot in the head by the Taliban, as child, while risking your life to get an education and speaking out on unjust inequities, then turn international activist (Malala Yousafzai), your medical condition (or the circumstances surrounding it) become fodder for your admission story. It’s not “getting shot in the head”. It’s that she got shot in the head for speaking out as a youth activist, THEN turned to the international stage to continue the message on a broader scale, in spite of the continued risk to her life. She is an activist. She demonstrates a commitment to cause. She’s a risk-taker. She works with international organizations to try to change the tide. She’s not a bullet wound to the head. She’s a very bright young woman with passion, demonstrable purpose, and determination, who gets results. She’s a Nobel Prize laureate, in spite of what happened to her. I’m using this example to demonstrate the difference between an unfortunate circumstance as a “hook”, and just an unfortunate circumstance that won’t help you gain access to extremely selective universities.
Having a chronic illness is unfortunate. It is not, however, a “hook”. What you do, or what you’ve done in spite of misfortune might pique the interest of selective schools. However, it’s probably a good idea to look a little further and a whole lot deeper than the prestige sheets.