My dog has red bumps, cracked nose, and a swollen eye. What's wrong?

It sounds like Charlie needs to be examined by the veterinarian. Those spots and the lesions on the muzzle could be several things including ringworm (which humans can get) allergies to something in the environment, food allergy or endocrine disease. Each one of these problems is detected and addressed differently and I recommend to discuss with your veterinarian which one to start hunting down first. Ringworm is diagnosed at the vet's office by examined the hairs. Food allergy is best ruled out with a diet trial using a hydrolyzed protein. Endocrine diseases are detected with blood work. Environmental allergies are a little more difficult to detect but a response to therapy or a blood test can give an indication. Once you figure out and address the underlying cause, the lesions should not come back. There are a couple things you can do at home and they can help but they may not address the underlying cause. You can try adding in an omega 3 fatty acid supplement for dogs, this can help improve the skin health. You may also try changing his diet to something like Royal Canin or Nutro as they are aimed at skin health. Also protect the area from trauma by having Charlie wear an elizabethan collar at all times if he is trying to lick or scratch the lesions. Best of luck and please feel free to post any additional questions.