Hello There are many causes of redness like allergy dryness, infection etc It is very difficult to comment without examining him Kindly share photos of his eye so that I may guide you better because need of any medicine is determined by the disease Once the diagnosis is confirmed then only we will discuss need of any medicine

Can't comment whether the medication is required or not without looking at the eye itself .Although there is no harm in putting it , for a week to 10 days