Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian.
My understanding is that Misty has been diagnosed with a collapsing trachea and that it is controlled with Tramadol (a opiod based pain and anti-tussive medication).
Now Sammie, your other dog also has a cough and you are concerned that he too is developing a collapsed trachea.
A wheezy cough can be a sign that of heart failure, heartworm or lungworm disease, a mass in the lungs, or that he has picked up an upper respiratory infection (like kennel cough). It can also be a sign of a collapsing trachea. He should definitely be seen by his veterinarian to re-evaluate him because it can be hard to tell without testing the primary reason behind the cough.
If his cough is productive, his gums are blue/gray and his respiratory rate is very high we shouldn't suppress his cough and it may be best he be seen on an emergency basis.
However if it is the typical dry hack/honk cough that goes along with kennel cough or tracheal irritation or collapse and he is eating, drinking and feeling pretty well otherwise we can use human products with dextromethorphan to suppress his cough. Dextromethorphin does have sedative effects so he may be a bit sleepy.
Robitussin DM or Benylin Expectorant are two good products. Use only products with Dextromethorphin or Dextromethorphin and Guaifenesin. Never give those with Tylenol (acetaminophen) or Ibuprofen or a decongestant as those are toxic for dogs. Give 1 teaspoon per 20 pounds of body weight every 6 hours. The side effect most commonly seen is sleepiness.
As far as controlling his tracheal collapse, if that is what he has, try to keep him as quiet as possible. The more active he is the more he will cough.
Use humidifiers to moisten the air that he breathes as that is soothing to his airways. You can also take him into the bathroom with you when you run a hot shower or bath.
Keep his teeth and gums very clean with brushing and antibacterial oral rinses (such as CET rinse). The more bacteria in his mouth the more he breathes the bacteria into his airways which leads to more irritation/inflammation and coughing.
Keep him on the light side, the heavier he is the more pressure on his pharynx, airways and chest and the more he will cough.
I recommend using a harness rather then a collar as that will be less irritating to his trachea, putting less pressure on his trachea.
A collapsed trachea puts stress and strain on the heart and reduced amounts of oxygen in the blood with a collapsed trachea can lead to heart disease, heart failure, and organ disease. So while the condition itself isn't deadly, unless the airway completely collapses and no air is moving, the stress on her heart can be harmful and lead to deadly heart failure or other organ failure from low oxygen levels.
Best of luck with your pups, let me know if you have any further questions.