Usually it doesn't affect the growth much.You can prevent by nebulizing the child always without using the antihistamine syrup and steroids.If it is uncontrolled asthma,you must use steroids,that can do more damage to his growth.Steroid pills or syrup may cause stunded growth.But this can also be prevented using inhalers.The inhaled steroids are very safe, and the children treated with inhaled steroids with a minimum/prescribed dose have stronger lungs than other using steroid pills and syrup.Once he is stable on it, these issues go away.