The same thing happened to my now late cat when I first brought him home. He was full grown, not a kitten, but the symptoms are similar, almost exact. It was due to the excitment of the move, plus new food, everything just upset his poor system :[ so we confined him to the bathroom for a few days, made sure he was drinking and eating, and spent lots and lots of time with him to get cuddles in and make sure he knew he was loved. It took him a few days before things got back to normal, and he returned to his happy, healthy self.
Its probably just the change in environment but most likely a change in food. Hope he's doing better!