Robert M. Gary writes:

No, when they test you for allergies they don't tell you which part of
the skin they put which allergen. It would be pretty tough to only
break out in certain areas.

True, but when you see someone open a bag of nuts, you know that the allergen
is at least theoretically present. Asthma, for example, is famous for being
an allergy that can be triggered not only by actual exposure to allergens but
also psychogenically, and allergic reactions in general are in a category of
physiological responses that are strongly influenced by emotion and mental
state.

In any case, if a person develops a dangerous allergic reaction just by having
a bag of peanuts opened nearby, it does not bode well for a medical, as I've
indicated, because, as others have pointed out, the previous person in the
aircraft could have eaten peanuts or a Snickers bar, and so on. Someone that
sensitive can scarcely risk walking down the street or going into any public
place.