Rhinoviruses, which are the most common cause of colds in humans, are not transmissible to dogs. In fact, it's pretty safe to say that there are virtually no "cold"-type viruses that can pass from people to dogs (or vice versa), so the puppy did not get this from your son. Just as in people, there are no common/safe medications that will speed resolution of upper respiratory viral infections. There is the possibility that this is something like Bordetella/infectious tracheobronchitis complex, so it is definitely worth a trip to the vet. NEVER give a medication to a pet without consulting a vet--many human medications are toxic to cats and dogs, and even the "safe" medications may be dosed very differently in a pet compared to a human. Even fruits can be problematic--grapes and raisins can be toxic to dogs. Finally, make sure the puppy is well vaccinated: distemper, a really nasty and frequently fatal disease, can initially look like a cold, but is a really preventable disease with appropriate vaccination.