For a child with a cold and runny nose, the cause is usually a viral infection like the common cold, and antibiotics such as Azithromycin are generally not needed or helpful because they work only against bacterial infections. Giving antibiotics unnecessarily can lead to side effects and antibiotic resistance, so they should only be used if a doctor confirms a bacterial infection. The best approach is supportive care; ensure the child gets plenty of fluids, rest, saline nasal drops for congestion, and steam inhalation if appropriate; for children above one year, a little honey may help soothe symptoms. You should consult a doctor if the child develops a high fever, ear pain, breathing difficulty, poor feeding, or if symptoms persist beyond a few days.