Using a piece of cotton wool with cooled boiled water is advice given to treat a young baby with gunky and infected eyes like conjuntivitis. It is not likely to be detrimental in treating an older child nor an adult.
Only a clean piece of cotton wool that is wet by the cooled down boiled water used only once on one eye and a new clean piece used for the other eye.
If your son's eyes have not settled, make an appointment for him to see the doctor. He may require some antibiotic eye drops.
At home, do not share towels. Let him have a towel specifically for his yes. Boil up some water and cool it down. Take a piece of cotton wool and dampen it in the cooled boiled water. Let him wipe his eye from the middle near the nose to the outer edge, throw about the cotton wool and use a clean one to wash the other eye.
For sinus infections, he can do steam inhalations. Take care not to get scalded. These should be done 4 times a day for a duration of 10 minutes each time. You can also put in a bowl of hot water in his bedroom with some Vick or olbas oil in making sure it is out of the way and cannot be knocked over.
Best wishes.
Has he been checked to make sure it is not pink eye?