Jarvis started with a limp in his hind leg. Before too long he couldn't even hold his head up. It was obvious any movement was very painful for him, so yes, AIHA causes pain and stiffness. At first, the vet diagnosed arthritis and treated accordingly but his symptoms got worse until eventually it was too late - he had to be PTS. If diagnosed early, AIHA can be treated with the dog going into remission.
Please, please don't worry. The reason I'm telling you is so you can be armed with a little more knowledge and ask more questions. I really hope Cooper's problem isn't serious. Of course you must do what you think is best, but knowing what I know now, I wouldn't give Cooper any medication at all tonight then get him to a vet in the morning if there's no improvement. And ask the vet about AIHA and pacreatitis, they take more notice of you if if you have some knowledge.
Please let us know how you get on. xx