No,approach is not correct. She probably has asthma,which is due to allergy,and antibiotics have NO role. When old,give just steam inhalations for cold and cough and decongestant nasal drops for nasal block or increased cough on lying down. Ideal treatment for this is nebulizer therapy,if not responding to steam inhalations alone. For this,plz consult your paediatrician. Influenza vaccine helps in such children.