As you told the symptoms and treatment, probably Baby has childhood asthma. Most common cause of not responding inhaler is noncompliance and improper way of giving medications. Always use spacer and mask with inhaler. Sometimes associated illness like allergic rhinitis (cold) also should be treated. Yes inhalers are the treatment of choice for childhood asthma. They are not for the cure. They help to keep the child symptom free and to live their normal regular activities like sports.