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Without further information it is very difficult for me to provide the best advice but I will certainly try. Please reply when you can and we can continue the conversation.
Coughs aren't uncommon in young dogs and we don't tend to worry if the cough has not been present for over a week and if the dog is otherwise well. Their breathing should not be affected.
There are many potential causes including:
Do ensure Prince is up to date with his lungworm prevention.
As he may be contagious to other dogs, keep him away from them for the duration of the cough.
Ensure the air is well ventilated and free of dust, smoke and cooking fumes.
Offer a teaspoon of honey every 12 hours.
Walk Prince using a body harness rather than neck collar.
If he has other signs or the cough is not resolving, he will need to see a vet.
I hope this has been useful and please feel free to keep me updated on how Prince is getting on.