That Coughing Old Dog Has "Old Dog Lung":

Something about Old Dog Lungs:
The cough is a synthesis of FIVE things - Read the list with sensitivity to what we can do anything about (heh heh)
1) This is a small breed - and there are narrow spots in the airway like the sinus/nose, plus the trachea, this prevents really good sneezing / clearance of airway slime.
2) This dog is elderly and that means the airway has "slimy" air-tube juice, (you can look at the spit in the mouth) which is bad juice to try and clean itself. Instead of thin, watery juice like when they were a kid. (see: "muco-ciliary-escalator" ala Google for more, nerdy information)
3) Any old dog's heart is enlarged by advanced age and in small-breeds, their genetic origins (problem #1 and #2). This takes up lung space and creates #4 next.
4) The trachea has a narrow spot, a very narrow spot where it pinches past the big heart #3.....The trachea collapses or closes when they try to cough. That means they can't *really* clean out the airway which is slimy to begin with.(#2) (Google nerds: "Collapsing trachea canine".)
5) Some dogs are always getting germs in a 'mist' from their teeth and gums. The germs get into the slime in their lungs and isn't cleared and they can barely cough it up, because of #4.

We can use antibiotics for #5 and that helps #2 somewhat, as well.
We can use cough suppressants for comfort and sleep and to prevent the #4 trachea getting flatter.
We can use anti-inflammatories like Temaril to thin the airway juices and REDUCE their production - #2 and reduce inflammation in the airway from all the coughing and stuff stuck in the airway slime.
We can't shrink the heart, and don't know for a fact that we have to. We can't widen or un-flat the trachea except via surgeries and MAN those are "special" kind of invasive. Those are big problems and we can only cope with the rest of it.

Sometimes Robitussin Helps?

You said my dog has: "Next Level Old Dog Lung" What's that?

Some dogs have "all of the above" with two additional things. Some dogs are inhaling germs into their mouth FROM their teeth. There are lots of fancy ways to tell for sure: but the best two are: Xrays and Transtracheal Wash. That's only $21,000 at Franchise Vets when you factor in the Neurology Consult, tests mandated by 'corporate' and the other, commission-based add-on tests. The second 'additional thing' is 'extra-medicine' meaning there are more medications which can bear on the case, and even hot-air-humifiers.