Even though his attitude is good you may need to regulate his level of activity until he is eating on his own. The hack/gag that you describe is an indication of inflammation or infection in the back of his throat. You can begin home treatment as follows.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 0.1ml 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. After examination your vet may choose to begin antibiotic therapy. While a single 10 day course of antibiotics defeats many infections it is no surprise that some puppies require treatment for longer periods. If your puppy has improved on the antibiotic it should be continued, if he has not improved your vet may change to a different antibiotic. It is sometimes necessary to continue therapy for several weeks. In my experience clavamox is often disappointing.
Please keep me informed.
We need to see improvement in his appitite in 1 day.