first: spay her. this will PROBABLY help to cut down on aggression issues with the new cat.
second: go younger. older cats seem to accept younger/smaller cats better.
third: i would wait until after the move, just because bringing home a new cat prior to a move is a LOT of change for that cat to handle, and you’ll want introductions to be slow (at least a couple weeks of no-contact aside from sniffing under a shut door).
in the interim, research methods of bringing a second cat into the home. there’s a lot of info out there, and doing it right can mean the difference between getting along and wanting to kill each other.
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.