Our Australian Shepherd (Jack) Has Been Coughing (really Hard Honking

Our Australian Shepherd (Jack) has been coughing (really hard honking kind of cough that causes him to gag and spit up white mucus) especially after he runs or gets active. Our vet diagnosed him with bronchitis and prescribed antibiotics for 15 days. At first it seemed to be helping Jack and he had more energy, but that didn't last and he is basically back to where he was before the antibiotics. Do you have any suggestions?