I am copying a recipe that I recieved from my Vet. It indicates that you should maintain this diet while providing distilled water. Then gradually expose the dog to foods one at a time (beginning with tap water) to discover what the dog can eat (without a reaction). I found it interesting that tap water could be the culprit, but water does vary from one location to another. Anyway, this may be worth a try...
Canine Hypoallergenic Diet (from Hill's Pet Products):
1/4# (.11kg) lamb, diced
1C (150g) rice, cooked
1tsp (5ml) Oil (it lists vegetable, but others should work as well)
1 1/2tsp (7grams) dicalcium phosphate (aka one Tums)
Trim fat from lamb, cook thoroughly without seasoning. Add remaining ingredients and mix well. Keep covered in the refridgerator. Makes 2/3# (.30kg). plus a canine multivitamin/supplement
Analysis
Protien ... 7%
Fat ... 10%
Carbohydrate ... 14%
Moisture ... 66%
Metabolizable Energy ... 795kcal/#
(I am not a scientist... but, it is my understanding that the average 20# dog requires ~400kcal/day, so I would think one recipe per day(?).)
Feeding Guide
10# ... 1/2# (.23kg)
20# ... 1# (.45kg)
40# ... 1 1/2# (.69kg)
additional notes:
I would recomend that you get a little notebook and begin making daily notes on what your dog eats and how it affects their activity level, alertness, etc. Any observations you can make. Also, don't expect to see instant changes in your dogs coat. It may take a little while before you see the situation improve. Keep that in mind, nothing you do is going to mean your dog will wake up tomorrow with a beautiful coat. it takes time.