Welcome to Just Answer. I'm sorry to hear about Frankie's situation. Honestly, one of the most common reasons for scratching is fleas. You may not physically see them and they could still be there. If he's scratching at his ears, then it could be ear mites. I would recommend having him checked over by a vet if you haven't done this yet. They can start / set him on his needed preventative health program including vaccines, heart worm prevention and de-worming schedule. It is good that you've been feeding the same food. But, some will have diarrhea due purely to the change in environment. He's been stressed due to the move. Could he be getting new treats as this can also cause loose stools. The other possibility is intestinal parasites and this is something your vet can screen for.