Thanks for the quick reply.
While I cannot diagnose this over the internet it would come as no surprise to me if your Chihuahua has some form of upper respiratory disease such as kennel cough. Since kennel cough is a strong possibility from your description I will tell you what I know about it ...
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, these dogs are usually otherwise quite bright and alert.
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 dogs 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 out sooner rather than later as antibiotics may well get him better more quickly and there is not really much you can do on a home treatment basis.
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