You did not mention the age or breed of your dog. Also, he is current on his heartworm testing and preventative?
If he is young and has been healthy, and is not having any changes in his breathing pattern between the coughing episodes, there is a good chance that you may be dealing with kennel cough. Has he been around other dogs recently, such as at the groomer or at a kennel or even a public dog park? This is a highly contagious disease and spreads from dog to dog through the air. Luckily, most of the time it is not too serious, they just do a lot of coughing, but continue to feel good and eat well. Many of these dogs will go into a coughing spasm if you put a little bit of pressure on the under side of their neck over the trachea (wind pipe). On occasion though, it can turn into an pneumonia situation. We usually treat these with antibiotics and sometimes cough suppressants.
If your pet is older and/or has ever been diagnosed with a heart murmur, then I would be more concerned. Coughing can be due to a build of fluid in the lungs if the heart is not working normally and this is potentially much more serious.
Other causes of coughing would include bronchitis, or allergic airway disease, heartworm disease and collapsing trachea. There is a relatively new disease called canine influenza that can look like kennel cough initially but has the potential to develop into a more serious illness. There is a blood test that can be done, but it will have to be sent away to an outside lab and will take several days to get back.
If this is kennel cough, while it is not really an emergency, it is an infection and with all infections, treating earlier is better than treating later. Coughing due to a heart problem would definitely be considered an emergency as these dogs can get into a crisis quickly.
I would tend to err on the side of safety and have him seen this weekend. If your vet happens to have hours on Sunday and your dog's breathing pattern is normal and he is young with no heart murmur, it would likely be okay to wait until tomorrow, but I would hate to wait until Monday even if this was kennel cough as this just gives the infection longer to get established. If your dog is not current on heartworm preventive and you live in the south where heartworm is extremely common, take him in immediately.
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Gagging usually points to a problem in the pharnx (back of the throat) . If he is having a coughing episode and then it ends in a gagging and bringing up of the fluid, it could still be kennel cough, even though it looks different than his previous bout of kennel cough. If however, there is no coughing and it is just the gagging, it is not kennel cough.
Usually when there is just gagging, we will try to get a good look in the back of their throat. This may require sedation as even the most cooperative dogs usually won't let you do a complete exam that far in the back in the throat. Sometimes, especially in young dogs that tend to chew on things, and the problem is just some irritation that is evident on exam. On occasion, I have removed pieces of grass or plant material fromback there. Once I removed a sewing needle from the back of the throat.
I have also seen this type of thing when dogs have been running with a stick in their mouth and then trip and the stick gets jammed in the back of the throat.
It sounds like the heart problems are not likely given the age of the dog, so that is good.
Again, although this does not sound like a life-and-death type of emergency, if there is something stuck back there, the sooner it is addressed the better, so I would still probably take him in this weekend. If you can think of anything he may have chewed on, be sure to pass that information along to your vet.