Hi Yorkiemom2,
My baby Nina had a terrible cough days ago - we went to a dog't birthday party and someone gave her food that was maybe too hot irritating her little throat. She was coughing so hard, that it let her to vomiting. I actually took her to the vet because of the vomiting and the vet told me that her problem was the coughing. The vet recommended that I give Nina Robitussin DM (dextromethorphain) as needed using a seringe. For my puppy, who weighs 6.8 lbs, the proper dosage was 0.6 ml. I asked about side effects and she told me I should only expect sleepness.
For her upset stomach, the vet recommended Pepto 0.3 ml 2-4 times a day as needed.
I hope your puppy feels better. If you are not confortable with giving him Robitussin, I recommend that you see a doctor.