Sorry about your poodle! It's been so long that I sort of doubt it is due to the tooth issue two weeks ago. My vet calls that itching insanely at a spot a 'hot spot'. I would try to get him in to be seen by the other vet if yours is gone for a while. Sooner the better. Here's some information. https://www.petmd.com/dog/care/evr_hot_spots_what_are_they The vet can prescribe some topical cream that will clear it up. Let me know what the vet says!
Sometimes they nibble at the skin in a place where there is a pain. It's not always an itch.
Maybe you could gently probe there with your fingers and watch his reaction? That should tell you if it's a pain or an itch.
If he has history of allergies, maybe it is an allergy to something? It could be to a new food (?) ....something he has been bitten by outside? I know that at this time of year if it is humid, things will bite. I often get insect bites in the Autumn.
Or it might be a delayed reaction to the anesthetic/pain relief he was given? I feel that it can take a couple of weeks, sometimes even longer for those drugs to fully leave the system.
But not eating....that is a red flag. A dog will want to eat (unless he is normally on and off with his food?
I would definitely tell the vet about this. An itch won't usually stop a dog from eating!
Yes they can get obsessed with picking at an itchy spot, and go a bit crazy with it, but the smell of nice food should usually distract them.