benadryl in some dogs (45% or so) can help reduce some of the symptoms of tracheitis (coughing, irritation) by sedating him a little but can do nothing to reduce the swelling. The best thing would be getting seen at your regular veterinarian and start on some cough suppressants and antibiotics to stop the trachea irritation. In the meantime you can safely try benadryl to make him more comfortable at 1mg per lb (a 10lb dog would get 2 childrens capsules twice a day) each childrens capsule is 5mg
This breed of dogs can develop what is called a collapsing trachea which is commonly manifested by a dry honking cough especially when excited lasting a few mintues. A good physical exam at a vet can help distinguish this from just tracheitis.
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