So glad your dog is feeling better now. You have given me hope. My little puppy is just over 13 weeks old, we have had her for 6 weeks and she has been ill the whole time.
She came to us with a cough and runny nose and the cough has never disappeared. She has had 2 rounds of antibiotics. The second set was given because the vet advised the cough has went into her chest. When we went back her chest was clear and she was only really coughing when she woke up.
The vet gave her, her first vaccination and she has gotten worse since then. We are back to square one.
I have been doing the steam with the shower and she has occasionally brought up white phelm but only a handful of times in the 6 weeks.
Like yours she eats and generally sleeps well (minus the coughing fit a couple of times during the night) and plays great!