I guess that depends how hard you pulled. If it was more than simply sliding him across the rug then maybe.
I think the best advice is if you think you've injured your chinchilla to get a vet appointment so they can take x-rays and be sure everything is okay.
It could just be you are feeling a normal feature of his anatomy there that you've never observed before. There's a transition underneath the skin where the vertebrae attach to the pelvic bones. This area is strong enough to actually hold the weight of the whole animal without injury.
A chin's tail has a column of vertebrae inside that can be dislocated but it usually occurs further down the tail. Normally this is associated with considerable swelling. I would expect it to feel like a lump if it were dislocated and this is very painful and would likely cause your chin to get depressed as the inflammation gets worse. It can grow pea sized or larger and if this happens the swelling can potentially cause dangerous complications cutting off blood circulation, causing infection, shock, death that sort of thing. So you might want to monitor this over the next few hours for changes.
