Ah, you must be feeling miserable and this has to be hard on you.
The nose would run if there were a fungal infection, a tooth or gum infection, something foreign stuck in the nasal passage or if he had a problem with allergies.
A tracheal collapse can be hereditary. You can see how it happens here
Bronchitis would cause coughing and wheezing
this breed is also prone to brachycephalic syndrome, so I wold check the gums and make sure they are pink and not blue or grayish. you can find more on this here.
Sometimes steam from a shower can make the lungs feel worse. If you have a cool mist vaporizer I would run that in a room minus any medication in it, just plain water.
I would take his temperature rectally and make sure that is normal. IF there is a fever then it would be a good indicator of an infection in the body. Normal for dogs is 100.5 to 102.5. If he has a fever you can start to reduce it by laying cool towels on the abdomen and keep checking the temp. once it starts to drop stop the towels.
IF he is eating and drinking normally it should be able to wait unless he is really showing signs of severe breathing distress. You looked at the reverse sneeze and you feel it is not that correct?
You wold see improvement on the novo Lexin only if there is a bacterial infection as it is an antibiotic and it only helps bacterial infections. One of the side effects of this drug is difficulty breathing. http://www.camroseanimalclinic.ca/novo-lexin.html