Anorexia (not eating) and vomiting in a dog is very serious. He should be seen by a vet within the next 12 hours ideally. This could be a vius, bacterial infection, pancreatitis, foreign object in his stomach etc.
A 13 week old puppy who is vomiting and off his feed needs to be seen by his vet ASAP. Is he up to date on his vaccinations? Vomiting and going off their feed is one of the first symptoms of distemper or parvo.
What was the puppy seen by the vet for on January 2? I'm guessing you meant that it was January 2, 2012 and not 2011 since he's only 13 weeks old? Just need to clarify that.
Ghilly