Cough in a case of allergic rhinitis
may be due to allergic bronchitis
or it may be cough variant of asthma
Cough which is aggravated during sleep should be investigated for gastroesophageal reflux.
I would suggest you to consult a pulmonologist
for pulmonary function test as it will help in diagnosis of cough variant of asthma and Serum IgE level to diagnose and follow the allergic problem.
Also get a GER scan done to rule out gastroesophageal reflux. Avoid cold,allergens( like dust, smoke, moulds, pollens, perfume, deo etc) and irritants as a preventive measures.