All cats throw up occasionally so there is nothing to worry about. But keep in mind that it should not be grayish color in vomiting. Otherwise it would be hairball, which is required treatment immediately. Yes there is a possibility that your cat is throwing up due to that mouse. But all you can do in that case is let it vomit so that all poisonous material can come out of it in case that mouse was poisonous somehow. There can also be overeating that is causing your cat to vomit. Watch only a day and then take it to vet if condition continues.
