The rash sounds like a skin dermatitis such as staph dermatitis or yeast dermatitis. These skin conditions are generally seen with allergies. Staph usually occurs on the lower regions of your pet and tends to have small pimple type bumps. Shampoo containing Chlorhexiderm and/or Oatmeal can help with this condition. Yeast typically shows as a greasy area that has a sweet musty odor. Sometimes the skin can become inflamed, darker and thickened due to itching. Yeast likes areas such as between toes, armpits and ears. Selsun Blue Shampoo can help with Yeast dermatitis. When shampooing, lather and leave on 15 minutes before rinsing. These shampoos are not meant to be a cure, just a relief until your pet can see a Vet. Benadryl can be given to your dog, the dose is up to 2mg per pound every 8 hours for itching due to allergies. You can read about allergies here: http://www.nhahonline.vetsuite.com/Templates/ContentPages/Articles/ViewArticleContent.aspx?Id=864
Here is a site that goes over itching in dogs.
Some dogs do suffer from dry skin and this would look a lot like dandruff. Fish oil capsules can help with dry skins and improve the coat as well. If your dog is drinking more and urinating more than normal, that might indicate a urinary tract infection.
Common symptoms of a urinary tract infection are frequent urination, dribbling urine, blood in the urine, squatting frequently to urinate, strong odor to the urine, inappropriate urination and straining to urinate as well as an increase in fluid intake.
A dog with a UTI does not always show all the symptoms and typically displays 2 or 3. I believe you need to have your Vet check your dog out so it can get medication for the problem if your dog is displaying 2 or more of the above symptoms..
Other causes for increased thirst and frequent urination include kidney failure, diabetes mellitus, cushing, a uterine infection (called pyometra), and liver disease to name a few. You can read about this here:
I hope this information is helpful to you.