It depends on the nature of the qualifying limitation-- and how persistent that limitation is.
That is, will mitigation or coping skills which develop through adolescence eventually cause the child to be more or less unimpaired relative to peers? Or not?
With anaphylaxis history, it's fairly clear that the answer will always be "not." That is, a factor which isn't a factor for most peers can cause havoc educationally for a student with life-threatening food allergy. Diabetes would be another great example; it's not enough to have great management, because occasionally factors outside of your own control will impact the condition and cause things to spiral OUT of control.
KWIM?
A college or university will have an office/individual that deals with accommodations and ADA compliance. Contacting that person early on is important, but self-identifying TOO early (in application materials) may be unwise.
We're in the process of doing this right now. I'll let you know how it goes. I know that several other members have done this over the past decade. Maybe Boo or Peg would weigh in? Ginger and Bensmom will also be going through this same process this year, as all of us have graduating seniors this year.