If you've never heard insects sneeze, there's a good reason
for it: they don't. That would explain the lack of insect
cold and cough remedies at your local corner store.

The main reason insects don't display this behavior is that
they don't breathe through mouths and noses. Instead, they
breathe through little holes called "spiracles," (rhymes
with "miracles").

Spiracles are located on the side of the insect's body,
which would also explain the lack of tiny bug sweaters, as
such fashions would surely cause the insect to suffocate.
The spiracles are equipped with valves that keep out dust
and fluids, so sneezing or coughing isn't necessary to
remove irritants.