Why is my puppy always itchy, losing hair, and still has worms?

Submit a stool sample to your veterinarian to diagnose the exact intestinal parasites Juju may have. The appropriate dewormer can be dispensed afterwards and repeated in 2 weeks. You'll need to submit another stool sample to confirm resolution. Keep him away from areas with feces and pick up his stool immediately to prevent reinvention. A monthly preventative, such as HeartGard, will protect against heartworm disease as well as the 3 most common intestinal parasites of dogs (hookworm, roundworm and whipworm).
For the itch, use a monthly flea preventative, such as Frontline, K9 Advantix or Revolution, for at least three consecutive months. Do this even if you don't see any fleas. In a sensitive dog, just one flea bite may cause severe itching. Vacuum everywhere and wash all bedding. Use an area treatment, such as Knockout ES or Indorex, to treat fleas that may be living in the environment.
You may need to have your veterinarian perform skin scrapes to check for mites which can cause itching and hairless. Discuss allergy testing, hydrolyzed diets, antihistamine use and food elimination trials with your veterinarian in case there is an allergic component to the itching.