Hi S.,
Trust your motherly inutition and give your child the benefit of the doubt. I would say that this is a physical problem and not a mental one. That's a weird diagnosis. Sounds like your pedi just doesn't know what it is. Especially because it started out as a cold, common sense and logic would point to an ongoing organism present.
It is possible that there is something irritating his passages? Did it start at school? Is the school moldy or does it have leaks from rain? (you can have fungal growing and not see it) are there animals in the classroom?
Some kids have allergies to foods that can cause mucous buildup in the mucous membranes.
My father had the throat clearing thing for years, it was real bad.. His doctor told him it was coming from his sinuses. However, it seemed like, and my dad felt like, it was coming from his lungs. It was coming from both. My dad had asthma as a kid. Turns out the throat clearing was related to milk products. Milk can increase mucus and cause inflammation in the mucus membranes.
You can try to build up his immune system. Give him fulvic acid, vit b complex (regulates nervous system) and vit A. Vit A is for the thymus gland, and the thymus gland is the center of our immune system. Cod liver oil is a good source of vit A. Give two doses a day.
We had a Minah bird when I was a kid. He talked up a storm, then ...he quit talking. My mom took him to the vet, and the vet's diagnosis was that he was bored with his food and to change his food type. The bird died a week later. I'm always amazed at the brazen absurdity of doctors.
Keep looking for answers, and blessings to your family!
Gail