Elevating the head at bedtime is a good option, as well as irrigating your child's sinuses with nasal solution. Often coughing occurs because the nose is running backwards down the throat. Saline should be used as often as possible, more than 3 times a day. There is no maximum for the use of the saline solution
If the symptoms still persist after 1 week, the problem could be related to seasonal allergies. I recommend that you consult your pharmacist who will be able to suggest effective products to treat the problem, if necessary.