Is an allergy a respiratory disease?

No: Allergies are not respiratory diseases. They are over-reactions of your immune system to specific proteins. The chemical cascade that results from this overreaction can manifest as wheezing, difficulty breathing, throat closing up, tongue/lip swelling, skin rash, etc.

Allergy is..: Allergy is a systemic disease that may affect one or more systems including the respiratory system. The most common respiratory disease that is associated with allergy and subsequent inflammation is asthma.