M., it's way too early to have him checked by a dermatologist, but he may have Hyperhydrosis. I am 36 yrs old, and suffered from this condition until my late 20's. Basically, the body's sweat glands over-produce sweat. There are medications that can be applied to the hands and feet (when he is old enough to care or be embarrassed about it), but the cure I found was a simple outpatient procedure called a sympathectomy. It's expensive because insurance doesn't cover it, but it was the best $$ I ever spent in my life. If I had known about the surgery when I was a teenager, I would have begged my parents to have it, since I believe it would have changed my confidence level immensely.
The doctor who did my procedure has a website: The Center for Hyperhidrosis. His name is Dr. Reisfeld, and he is located in Beverly Hills. HE IS WONDERFUL AND CHANGED MY LIFE!!!!!
It might be worth an e-mail to him to see what he recommends. Good luck, and let me know how things go.