While there are many symptoms of allergy, watery/itchy eyes, sneezing, and a constant runny nose are some common symptoms. Cough, shortness of breath, and wheezing are common symptoms of asthma. Chronic cough alone can commonly be caused by asthma.
History is the most important first step. Physical examination, skin testing, and a lung function may be necessary. If you suspect you may be suffering from allergies, see an allergist/immunologist.