Hello, my name is ***** ***** I have over 20 years of experience as a veterinarian. I understand that you are curious about the effects and benefits of Pet Wellbeing Throat Gold".
Unfortunately I doubt that this product will be helpful for a dog with a cough or respiratory difficulties.
The FDA does not regulate naturopathic or homeopathic supplements, and as such many have little or sometimes none of the listed label ingredients. A recent survey of products on the shelf at Walmart and Target from supposedly reputable companies showed not a single supplement actually contained what was on the label, as far as ingredients or the amount that was listed.
Of the ingredients listed on Pet Wellbeing Throat Gold's label there are some that have been proven to have some positive effects, but not necessarily on the respiratory tract.
Ginger is known to soothe stomach upset.
Cherry bark has some anti-inflammatory properties when incorporated into a tea for people.
But licorice root can actually toxic for dogs. Licorice root contains glycyrrhizin, a natural sweetener, which can cause liver damage, raise blood pressure and cause muscle weakness. I suspect that the amount in this product is very low, but still it is not something I would give my dog.
In short I do not recommend wasting your money on this product.
You'd do just as well to give a little warmed honey mixed with a little lemon water to soothe a cough or sore throat until the primary disease process causing the cough can be treated.