Hi, Welcome to JustAnswer. I am a licensed veterinarian and I'm here to help you. Pulling on the lead excessively can cause tracheal and laryngeal damage, but usually it is inflammation and by discontinuing the pulling, the inflammation and coughing will discontinue.
There are 2 other ways to walk a dog on a leash. . .the Halty Collar which is actually around the nose. This is a slip collar (not a muzzle), and does take a little while for the dog to get used to it. The other is a non-pull Mesh Harness which is well accepted immediately. I'm sure there are other brands of both of these on the market.
I personally use and really like the Mesh Harness.
There are other causes of coughing and noisy breathing that can be more serious, so you may want to have your vet check for these: Heartworm disease, bacterial or fungal pneumonias, heart failure, foreign bodies in the tonsils, tumors, etc.
Is Jenny coughing pretty much all of the time? For how long has this been going on?
Jenny coughs intermittently for about 2 months now
Hi. . .thanks for your response! An intermittent cough could be from her pulling on her collar, but what makes sense to me is to have your vet there examine Jenny listening carefully to her heart and lungs. If you have heartworm disease in your area spread by mosquitos, I'd also have her tested for this. If Jenny's exam is normal and her heartworm test is negative, then I would try an alternative to a collar as I suggested above to see if resting her larynx and trachea resolves her coughing. Does this plan make sense to you?