If your pup is managing to eat solids then do not give him milk but give him water. You should never give dogs and cats cows milk. If your pup is not weaning very well then you need to see your vet for a special milk substitute while he completes his weaning. But please provide him with water at all times. .The milk you are feeding him is making him ill so please discontinue. There is widespread belief that milk ,and by this people usually mean cows ,is okay for all other species but this is simply not true.
