Answer:
Short-acting beta agonist PRN with low-dose inhaled corticosteroid
Step-by-step explanation:
Since the cough is wheezing and persistent and it affects the patient mostly everyday with symptoms occurring up to 3 to 4 days in a week, these are consistent with Asthma, but the mild persistent type. Such type of asthma is better treated with short-acting beta agonist PRN and low dose inhaled corticosteroid. Other signs of atopy are skin rash and swelling under the eyes as stated in the question.