It's not a neurological problem. It's an eye problem.
The kid's eyes are itching, and he is intuitively trying to "squeeze" irritating substance out of the eyes using eye muscle. He probably ate something that he is allergic to, or he came into contact with a caustic substance.
If he's shutting his eyes so hard that it hurts, this is a big problem. While it's unlikely that he will injure himself permanently, there is a small possibility of it.
This is not a nerve problem. Doctor only mistake it as such, because they don't understand the reason for the muscle contraction. They compare it to nervous twitch, but this problem is very different than nervous twitch. If your son says his eyes are itching, then you can be certain that there is irritant in the eye. Eliminate whatever is causing the irritation (diet/enviromental) and your son will stop contracting his eye muscle.