I'm going to have to assume you are talking about a respiratory infection here.
Sometimes there are emergency vet clinics available if you are willing to go the distance. The one we like to use is about 100 miles away. If it's a respiratory infection it might be your only chance to prevent it from spreading to the lungs and causing pneumonia, which, is almost always fatal in rodents. You will need stronger or different antibiotics, anti-inflammatory medications, and certainly an exam to determine the cause of the pain. It sounds like the antibiotics were not effective and the infection has returned. Pain is very dangerous to chinchillas and may result in anorexia and potentially shock.
Usually veterinarians prescribe oral antibiotics, in which case, there is a risk your chinchilla will stop eating because it can affect their bowels. It's important to have everything needed to syringe feed a recovery diet through the course of antibiotics. Some people lose chinchillas because they stop eating from antibiotics and they don't catch it. Much more than a day without food causes serious digestive complications that are sometimes fatal. Do not stop the course of antibiotics early.