I would take him either to an allergist or an ent (ear-nose-throat) specialist.
I'm trying to think what would be located in that area of the neck/throat and lymph glands is all that comes to mind.
If your son is complaining of pain, I would believe him. Sometimes, when a child's parents are divorced/separated, they are hurt over it and don't know how to talk about it, which can become actual physical symptoms. But I would still take him to another doctor. It would be terrible to assume it's nothing physical, and then something be wrong.
How is he handling you and his mom not being together?
Libby