If his present food is the cause it can take some time to get it completely out of his system when doing a food switch. It could take as much as 30 days but that would all depend on the culprit in the food and how long the dog has been eating it.
Its not common for such a young dog to have food related issues but it can happen.
if you don't see a change I would consider going to the vet for a skin scraping to rule things out. has your pup been to the vet yet for his inital health check since you got him home? This is very important, and if not, i would go now and have the skin issue checked as well.
Just be careful switching his food too soon upon his arrival with you. New environment, loss of littermates can cause stress and a diet change too can often cause loose stools or severe diarrhea.
Try to let him acclimate to his new surroundings for at least 2 weeks before making the change.
I would stay away fron corn, soy, wheat, sorghum and by products in any food. If his problem is food related it may be best to choose a food with a single protein source. chicken or Lamb but not both.
Not sure what is in the food you chose ingredient wise but if you decide its not right I would go with California Natural as it has few ingredients and can often work well for a dog with food issues/skin issues. Or I would consider a grain free but the only one, because of his age, would be the Natures Variety Instinct Rabbit formula as it is low enough in calcium for a growing pup.
Keep in mind when he is ready to go on adult food (I recommend 6 months) the Califor. Nat. adult will not be hi enough in protein at 21% for a growning pup so you will have to be ready with a different brand at that time.