Hello, thanks for your question today! I am Dr. Drew, and I am a licensed veterinarian. I'll be happy to help you in any way I can.
Asthma is not actually something that is a recognized illness in dogs, so I am quite suspicious of the diagnosis. Dogs can develop a chronic allergic bronchitis, which can cause coughing, but generally a steroid would have reduced the coughing to a significant degree, in the case of allergic bronchitis. Incidentally, true asthma is very responsive to steroid treatment, so in either case, it sounds like something is being missed here.
I would want to know if monthly heartworm prevention is being used, since heartworm disease can cause coughing. A blood test can be done to diagnose heartworms.
Water pills are typically prescribed when a cough is due to heart problems. If there's not a heart problem, then the water pill may be making the cough worse.
The next diagnostic steps in this case, after confirming that heartworm disease is not the problem, would be a Bronchoscopy, which is a procedure where a camera is inserted into the airways.
I would also consider trying a prescription cough suppressant such as Hydrocodone, in order to see if resting the airways may make the dog more comfortable. Over-the-counter cough suppressants are not as useful, but can be tried. Robitussin-DM
, 1mL per 10 pounds of body weight, every 8-12 hours, could be tried.