Most often cough and cold in children is caused due to certain viral infections. They are generally associated with an allergic component. Giving some antiallergic like Cetirizine syrup is likely to be more helpful. Unless associated with secondary bacterial infections, antibiotics are not required. Irrespective of use of antibiotics, it should take 5-7 days and you would have to be patient. Giving steam inhalation should be helpful. I would prefer a gap of a few days before he resumes his swimming lessons. This would actually help it from spreading to other children.