See your doctor. A bad cough with straining needs to be evaluated. We want to make sure your child is not wheezing or has bronchitis or worse. Once that has happened, we have a better idea of what to do. I know of some great chinese herbaceuticals and homeopathic remedies for cough, but I would want to evaluate a cough like you describe first.
Take him to doctor. If he is having that much trouble when he coughs, his doctor needs to see him to make sure it's not something more severe that a common cold.