Hi and welcome to Just Answer. The common flu is not passed from human to dog or vice versa. IF your dog is having problems breathing he could have bronchitis, an upper air way obstruction, a virus , tracheal collapse, a fungal infection, a bacterial infection, any of the above would require treatment from a vet.
The only other thing that would cause similar to wheezing or gagging would be a reverse sneeze which is harmless. You can see a video of one here and compare it with your dog. There is usually more reverse sneezing this time of year as people start to put their heat on. http://www.youtube.com/watch?v=1UyBrb0Hhpk
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
Licking of the lips could be due to nausea,as could drooling, and both would be a side effect of the medicine if he is on that.Wheezing would be more a sign of bronchial problems. To say what it is would be very difficult. I can only tell you how to check the vitals of temp and breathing, gums, all things that may deem this to be serious enough for vet care now. As for the temp there is no other way to tell if there is an actual fever other than taking the temp rectally. Many dogs will get dry noses or warm ears but it does not mean it's a fever which many believe.
Because the dog does not display every sympXXXXX XXXXXsted, does not mean that is not the problem, the symptoms are guides of things that may or may not be seen.
In giving yet another look at prone illnesses to the bulldog breed I am seeing laryngeal paralysis which can present gagging or coughing/noisy breathing. But again the gums would be a bluish color.
If you have used any new type of product on the floors, then that may cause a reaction, or any type of air freshener , Lysol etc.
I can only tell you that your flu would not have been passed on to the dog, and if there is problems breathing the dog should be looked at and while I understand your position, the best thing you can do now is watch him and check his heart rate, breaths per minute, temperature, etc.