If a college suspects your illness will prevent you from completing your studies in a timely manner, then, yes, it will factor in their decision and not in a good way. That’s why highly competitive colleges such as T30s expect you to have accomplishments above and beyond managing your medical condition. They want hard evidence/proof - not just your word - that you likely can not only manage your studies, but will contribute to campus and community life as well. And even that’s a minimum expectation for T30s.
Now as other posters have mentioned, there are a lot of US colleges with varying degrees of expectations that you would not only have a better chance at admissions, but that may offer better or more appropriate accommodations. But you only seem to be interested in prestige. That’s fine. You need to understand that those colleges are very likely to feel bad for you while still not admitting you. They aren’t interested in what happened to you (fibromyalgia) so much as what you made happen (your impact outside of you and your family). See the difference?