Well, different parts of the country...a LOT of vets in central PA (and I deal with a LOT of them) don't see everything as an emergency especially if it was already seen by one vet. Furthermore, a LOT of local vets here in central PA are friends. If I call my vet and say Dr. Hill (who's one town away) presribed this treatment but people on the internet disagree...my vet is going to tell me to follow Dr. Hill's treatment. Period. He doesn't have the time to treat an animal that's already been seen. Furthermore, him and Dr. Hill are social friends and a LOT of vets in this area do not want to step on toes by disagreeing with another vets prescribed treatments. Makes first vet look incompetent.
That all said, I'm not saying I know what treatment this chin has or hasn't received. Animals in pain should never be let go on an "it can wait" basis. Period. This is why we advocate having a good chin knowledgeable vet BEFORE purchase of a chinchilla.
Just the same, vets are different all over the country. I know some vets in the south are not allowed seeing an animal that they are not extensively familiar with. I know vet care in other countries seems very expensive because of their human's universal healthcare...I know that here "in the country" where I live...I've volunteered at vet's offices...and not everything we consider an emergency with our chins would be by the local vets. I've seen dogs with bones sticking out of their legs...waiting in holding pens (overnight) for treatment because it wasn't an emergency. No joke. I don't care who believes me. Things are different in the country. Vets stick together, and vets treat animals by priority...THEIR priority. What THEY see as an emergency. Even routine care...say my dog is due for her vaccines in June. I wait until may to call for an appointment...well...it's too late, she's going to get her shots late because stuff like "routine care" or cosmetic procedures (ear cropping) is NOT an emergency and can wait...for MONTHS.
To the OP, it is highly recommended by everyone on this forum you find and seek treatment from another vet. Even the same vet, if you return to them and demand treatment described in this thread...worth a try. I've demanded treatment based on my own knowledge...sometimes it's worked, sometimes not. Regardless, if you should never let an animal suffer in pain, you do everything you can. Period.