Most dogs are allergic to pure form of milk and your vet did the right thing by asking you to stop it right-away. In fact, your pup should never have been fed milk in the first place. Not sure who recommended that to you. Puppies have different system from human babies and I've seen people feeding milk to their puppies thinking they are young and then complaining the puppy is giving out loose stool and developing allergies.
The milk in pedigree you're referring to is in powder form and it's ok to feed to him.
I'm quite sure your puppy is not falling sick due to Pedigree as most commercial dog food are highly palatable and digestable. However, it seems there is some ingredient in Pedigree which your puppy's digestive system is not agreeing with. I'd suggest you to switch to other brand. When I brought my Labrador (2 month old), I fed him Eukanuba for one month and after that my vet recommended feeding Pzer's Canobites. The results were good as Canobites reduced the no. of times the puppy gives stool and there were no stinking smells from it.
Though, Canobites didn't make my puppy gain good weight and he was more muscular than heavy i, he had not developed any stomach issues.
If after switching another brand and should you notice no improvement and symptoms persisting, you can then conclude that commercial dog food is not for your dog and you should not feed it to him. But this will open a big scope of feeding home-made food to your puppy. Sooner or latter, I feel one should phase commercial food out of the diet and switch to home made one as its healthier and cheaper in terms of pocket.
I think, the time has come for your dog to be put on home-made diet altogether. Boiled egg is the best for your puppies. Apart from that you can feed curd which is highly palatable and keeps the stomach problems away. You can put him on chicken-rice as a main meal to be fed twice a day. I'd suggest feeding boneless chicken mixed with unpolished rice and served boiled. Curd can be fed two times a day and boiled egg ones in the morning.
I think, all these will suffice and will keep your dog happy and healthy. I tried all these myself have have witnessed results.
Any doubt give a shout, I'll come back again next weekend!