These are all wonderful schools with major credits and drawbacks to both. It is nearly impossible to do well in a school if you are constantly suffering and ill, so chose the one that will keep you as healthy as possible- you can’t really go wrong with such great choices.
Cornell would be tops just based on your concentrations, and the network you could accumulate there, however, it isn’t the best climate for a weakened immune system. I am assuming if you mentioned athsma it might be severe. You would really get to explore liberal arts at Brown, and have a great time, but underclassmen are required to live on campus, and most of the dorms are very old. If mold, mildew, or dust mites exacerbate your condition, this could be very difficult for you and you may need special approval to live off campus. Like Cornell, I believe you would be more likely to create an expansive network (I do mean people who will work in corresponding fields, not just friends) at Duke, and school pride and athletics would be enormous fun. Most of the dorms are newer, however “hayfever season” is longer down south. The upside is that in the south air conditioning is the norm, unlike in New England and that can filter some of the pollen out of your area. I’m only mentioning these as potential issues, you know your body best, and what you can handle. Good luck!