I'm sorry your chinchilla is not doing very well. I really hate to say this but your chinchillas diet is very unhealthy. Chinchillas should eat only high quality alfalfa based pellets and loose timothy hay. Treats of dried fruit can be given occasionally (maybe one really small piece a day) but should never be considered part of the diet. Personally I don't give my chins treats anymore. Such a diet that you describe can cause damage to their internal organs over time and tooth decay.
Matting around the hind quarters caused by drooling. This and preference for soft food indicates dental problems which are usually fatal in chinchillas.
You can try to have the teeth filed if the roots aren't too long. The roots of bad teeth can extrude into the eye socket and brain and this is very common and nasty thing to deal with. You should get an x-ray to make that assessment.
Usually having the teeth filed is a temporary fix and the teeth will have to be managed throughout the chinchilla's lifetime which normally isn't very long once malocclusion occurs. Dental malocclusion is a progressive disease. Rodent's teeth constantly grow and must stay perfectly aligned. As fiber (from an appropriate diet) is chewed the teeth constantly wear. If the wear is uneven the teeth will extrude outwards and cause damage to the inside of the mouth. These spikes, or spurs can be trimmed if found but unless the alignment of the teeth is proper will return.
If these problems are caused by diet and the teeth are overgrown because the animal is not chewing properly since it has been picking out the soft stuff there is a small chance switching to an appropriate diet and trimming the teeth may improve the condition. Most attempts at this are unsuccessful and you should not dismiss the option of euthanasia. Discuss this with your vet. Some veterinarians will try to convince you that one treatment is a cure. I've seen this and I've seen it fail and the owner gets very upset with the vet. Sometimes filing the teeth has no effect at all.
If these problems are caused by defect in the skull as many chinchillas are not bred properly and the defect is congenital euthanasia is recommended.
With that being said malocclusion, although the most common cause of these symptoms, is not the only possible cause. A vet exam is certainly needed.
You need to obtain instructions and supplies from your vet. See if you can at least pick up syringe feeding supplies and a recovery diet such as oxbow critical care without taking your pet in. If antibiotics are prescribed keep in mind this can also cause a chinchilla to stop eating and its food intake must be carefully monitored through the course of treatment. Syringe feeding is necessary at this time.
I hope everything works out well for you. I think you need to be very guarded about this one.
