I am very sorry for your loss. I feel really bad for you and I hope you'll feel better soon.
Pneumonia most likely caused this seizure not the medication so don't feel too bad about that. In fact that is usually the last thing that happens with pneumonia when the blood oxygen levels fall to a fatal level.
Chinchillas can thrive in temperatures near freezing. Unless you had the A/C blowing straight into the cage with unmixed cold air I seriously doubt the air conditioner caused it (In that case it still wouldn't be the cold but stress). I run my portable air conditioner constantly to keep the temperature at the cage between 75F-80F (Although below 75 is best practice) and my chinchilla is very healthy. It blows perpendicular to the cage so there is no draft inside. Pneumonia is not caused by being cold but caused by viruses, bacteria, mold, or sometimes internal diseases that invade the lungs causing inflammation and pooling of fluids.
Sometimes an infection may result from an underlying problem (even a tooth problem) that has caused them to drop below a healthy weight or during a period of high stress that causes weight loss and suppression of the immune system. If your chinchilla was underweight it may not have been able to fight it off. There are many microbes that exist in the environment that can cause this if the chinchilla becomes immunocompromised. When it is hot and damp outside these types of microbes become more abundant.
Best practice is to always weigh chinchillas once a week and keep a log. If you see a weight decrease more than 15% on the trend it is time to see a vet and get a diagnosis before it can no longer recover from infection or the anesthesia required for certain types of tests. Usually when a chinchilla starts acting sick it is too late, especially in the case of respiratory illness.
Again I am very sad for you and I am so sorry you lost your chin.