Each of the sneezes is an anagram of a common allergen with one additional letter added:
- RAGWEED + H
- BEE STING + I
- LATEX + S
- PENICILLIN + T
- DANDER + A
- DUST MITES + M
- POLLEN + I
- TREE NUTS + N
- SHELLFISH + E
The extra letters spell the answer HISTAMINE.