I would take him back to the vet if he is still coughing, especially as young as he is. He could have come to you w kennel cough. Here in the US they give antibiotics (Clavamox or Baytril) and sometimes cough suppressant (Delsym, Tussagon). It also could be a collapsing trachea. He is very young and tiny and could become very sick very fast, so again, I would take him back to the vet. He can have kennel cough and have clear lungs.
It does help if you have a video camera or a cell phone that videos to video one of his coughing episodes and take along to the vet. I did that when my Gidget had a cough, and it helped the vet be able to tell what was going on. She had kennel cough and allergies; put on antibiotics, cough suppressant and children's allergy med. Took about 2 months to clear up.
Wish you well w your little one! Please let us know how you make out! Welcome!
