Yes pleeeease don't take him outside too much, they are susceptible to everything right now and I'm assuming you haven't started him on heartworm medication as he is only 16 weeks old. First thing is first like Boopster said, take him for his wellness check and start his series of shots. They'll also take a stool sample to check and see if he has worms which is common in babies. You got him from a petstore so who knows where he could have come from
Make sure he's healthy before worrying about the training!