Is it common to have an allergic reaction in only one eye?

Possible: It depends on which eye gets exposed. Usually, both eyes get exposed, so allergic reactions are commonly bilateral, but if only one gets exposed then you will get it in one eye.

Not really common: While possible, it is not common to have an allergic reaction in only one eye. Exceptions include rubbing one eye (which causes and allergic-like reaction) and touching only one eye after being exposed to an allergen such as animal dander. It is pretty difficult to avoid touching both eyes, but if one is careful after the first eye's exposure, it is possible to avoid the 2nd eye reacting.

No: Allergic eye condition commonly referred to as allergic conjunctivitis from environmental causes would be expected to affect both eyes. If only one eye is affected this would most likely be due to exposure of the eye to a substance either intentionally or accidentally.