Thanks for the question.
In direct answer to your question : There would be two general possibilities here, it could be that your dog has contracted an infectious respiratory disease such as kennel cough
but be aware that heart disease
in the dog can present in the same way and your dog does have a heart murmer.
Kennel cough is a common contagious respiratory disease of canines. This disease is usually associated with recently having been in kennels or having been where dogs congregate, but dogs living on their own can sometimes catch it as well as it is an airborne disease.
This is a disease which vets will see quite a lot, we often have to explain the symptoms to clients :
1. Most owners whose dog has kennel cough think there might be something stuck in the throat due to the strange retch that these dogs have - a bit like a seal honk!
2. The dog may sneeze a little but the cough is the main symptom, some dogs are quite bright and alert but others can be lethargic during the course of this disease. The green nasal discharge would be a further sign of a respiratory infection.
3. The dog will retch for a few minutes and in the end it will be productive, he will bring up some white sputum, some owners take this for vomit. Once he has done this he will settle down for a bit.
4. It is normally not a serious disease but will run its course given one to two weeks without treatment, however antibiotics will speed up recovery and make your dog feel better very quickly.
Here is a link for more information on this disease : LINK
My advice to you is to have your vet check your dog over again out as soon as possible, there is not really much you can do on a home treatment basis if this is kennel cough that you are dealing with and as I said there are other possibilities other than kennel cough such as heart disease.
If I have not answered your question fully enough or if you would like to ask more I will be on line for the next hour or so and I will be pleased to discuss your question further.
Scott Nimmo BVMS MRCVS