Sorry to say that this might be, as others noted, a leak somewhere inside the wall, which is a total pain. If the drywall does not feel damp or show stains on the side you can see, that doesn't tell you much, unfortunately; you can't see or feel wet that's on the reverse of the wall or on the wood joists within the wall.
There are companies that deal with mold and moisture in homes. They can come out and examine the room to see if their devices detect moisture in the walls -- we had this done on a wall in the basement to see if a leak had leached up the drywall and they were able to test the drywall without cutting it, etc. I'd call a few such places and find out what they would charge (if anything -- they might consider it a "free estimate") to test and see if they detect moisture in the walls. Have them test the carpeting as well, if the room is carpeted. We have had to replace carpet and padding due to leaks.
The issue is -- a musty smell can be masked but if the source is actually mold, the mold must be removed professionally or it can cause real sickness, respiratory conditions, allergies, etc. If it's mold, smell is just the symptom of a larger problem, the mold spores that can make you and your son ill. Laundering things or pulling moisture from the air with "damp rid" products won't deal with the real problem in the walls or wood. So if this is a persistent problem and not just seasonal funk from a wet winter--I really would get it checked out, for health reasons.