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1.
Eye pain and puffiness caused initially by airborne irritants such as smog and dust commonly found in New York City -- sometimes lasting for days.

Colloquial term, common in the Northeastern United States.
Person 1: I woke up with a terrible headache around my left eye.

Person 2: Weren't you in New York City yesterday? You have Brooklyn eye. Get some fresh air and it should go away in a couple days.
by Prof. Whiskers April 15, 2009
 
2.
Eye irritation caused by urban pollutants
I can barely see! The LA smog gave me terrible Brooklyn eye.
by minidefiner July 27, 2009