You are describing gagging which is a sign of irritation in the back of the throat or larynx. If he feels good and eats well he will be okay. There are a couple things you can do at home to help. Using a nebulizer or a moist bathroom environment for 20 minutes 2-3 times daily if your puppy will tolerate it often is helpful. I also like using expectorants to help your puppy to bring up any fluid or debris created by the infection. Guaifenesin is a safe expectorant available as an over the counter syrup, I usually start at 0.5ml per pound of body weight, orally 2-3 times a day. Some veterinarians suggest using cough suppressants but while there may be some artificial improvement in the frequency or intensity of the cough it seems that overall the cough lasts longer. We need to recognize that a cough is part of the body's attempt to eliminate the residue left by infection in the airway, suppressing this natural response does not make sense to me. If your puppy is not improving or especially if his attitude or appetite are affected you should contact your veterinarian.