Find a good reputable dog dermatologist. Sounds like you may be dealing with both food and environmental allergies. Or you may find that it is neither. A dermatologist will be able to guild you. And it won't cost as much as you think it might... example... my last dog was scratching like crazy... so off to the vet I go... office visit, flea meds (no sign of fleas) back home. Week later dog is still scratching like crazy... back to vet.. office visit, skin scrapping, meds for mites (no sign of mites) back home. Week later dog is STILL scratching like crazy... back to vet... office visit, more skin scrapings, dip the dog, medicated shampoos, meds for sore spots, steroids, still no idea what is going on. Back to vet several times for dips... the dog is miserable and looks horrible! Her fur is patchy, her skin is red and raw. I cried she looked so bad. I finally had it (it would never have taken this long now... but I was young and dumb and trusted my vet) I got lucky and found a wonderful dermatologist. ONE appointment.. office visit, skin scrapping, medication, medicated shampoo and finally... a diagnosis! She had sarcoptic (sp) mange picked up either at the vets office or groomer. I paid for each vet visit... the dermatologist included follow up visits and believe it it was a lot less that I paid out to the vet. But the best part is she was able to give me that diagnosis quickly and the proper treatment so my dog could feel better.
Like I said... find a good dog dermatologist.
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