The condition described here sounds typically like bacterial conjunctivitis secondary to a viral inflammation. This definitely needs antibiotic treatment and some lubricants to decrease organismal load.
Next Steps
Please start your kid on Tobramycin eyedrops about 4-6 times a day.
Also start on eyedrops artificial tears 4-6 times a day.
Add syrup paracetamol to decrease the inflammation of eyelids and pain associated to make the child comfortable.
You also need to take care of cold. Give plenty of fluids to your child.
Make sure to maintain ocular hygiene by cleaning regularly with boiled drinking water at least 2-3 times a day. Also avoid anything else giving the eye especially hands. Maintain proper hand hygiene as disease may spread to other eye and other people.
Health Tips
Do meet up your ophthalmologist and ENT surgeons...