Your bird may be shaking because he is cold, is he in a drafty location? Does he fluff up his feathers too? When my bird does it usually means hes cold from the window or air-conditioner in the next room. He may also shake because he's excited to see you or because he's still scared that he's in a new place.
My bird has a bedtime routine that he likes to go to sleep when its dark and on a favorite perch, if I don't cover his cage when he's ready for bed he yells at me until I do! we have been able to leave him for one night (due to a family emergency) and I made sure that all 3 of his food trays were full including the largest one which is a dispenser. We also made sure he was in a room with a closed door separate from our older mellow cat who got extra food too. We also got one of those test-tube water bottles he likes that kind the best.
Good luck at the vet, hopefully he can answer some of your questions too.