crate training is something i’d look into, as well. if he cannot be trusted, then he should not have full access to your home. i agree with Dr. Magnifico, he needs a lot more work from you to keep his boredom in check.
eventually he may get an obstruction if you allow this to continue. obstructions are costly and can be fatal. nip this in the bud NOW.
It is still allergies, just less likely to be a food allergy. I would contact your vet by phone and inquire if they want to start him on an anti-histamine etc.
Good Luck
Dr Dawn
Just wondering…..Did your vet say what is causing the head shaking? Head shaking usually indicates an ear infection, but it could also be from a rash inside his ears or fluid in his ears like otitis media in children. This very likely is allergy related. Probally not a food allergy but rather something airborne like pollens or grass or dust or maybe something like a brand of carpet cleaner which is a contact allergy. I had a Chihuahua once that was allergic to the brand of laundry soap I was using. Maybe you can call your vet and see if he’ll be ok with you giving him benedryl and get the correct dosage from him.