I wouldn't use a cough medicine for a sore throat from the tube being in it. But you can try some sugar syrup such as Karo or Pancake syrup to see if that will sooth the throat and end the coughing. If you happen to have a popsicle or a low fat vanilla icecream a bit of either might also help with coughing by soothing the throat. Or if your dog likes ice cubes one can work. You can even make a doggie ice cube or two by mixing some canned food or baby food meat with waterand freezing it. The cold can stop the irritation that is triggering the coughing by reducing pain and inflammation.
When a human cough medicine/suppressent is used the one is Robitussin DM. Read here about cautions and dose info
Other meds may have ingredients toxic to dogs in them.
Hope this helps you!