A scratching puppy is certainly nothing to worry about -- unless it is excessive and leads to coat loss, red skin and, ultimately, infection. In that case, your puppy may be suffering from an allergy. Your vet can tell the difference between an allergy and normal canine behavior. If it is an allergy, you'll need to identify the allergen and then control that allergen or your puppy's symptoms as best you can.
A puppy could be allergic to any number of things.
In general, allergies fall into these categories:

  • Inhalant allergies: They are in the air. Pollen, for instance.
  • Contact allergies: Your puppy's skin is sensitive to something, possibly a fabric or a plant.
  • Flea allergies: The saliva is the culprit.
  • Food allergies: Although not common, some puppies react to ingredients in their food. Don't change your puppy's diet except under the direction of a vet after other allergens have been eliminated as possibilities.
  • Uncommon allergies, like hormonal hypersensitivity, in which a puppy is allergic to its own hormones.

The goal of treatment is to control symptoms and make your pet comfortable. Usually that can be done by avoiding the allergen. If the allergen can't be avoided, medications or a series of injections forcing the body not to react may be in order.