My GSD has the same skin problem about a year ago too since she was 15 weeks. It lasted for about 4 months and she is ok now.
During the 4 months we have tried the following:
1. Antibiotic from Vet - Works instantly but eczema comes back after antibiotic runs out.
2. Vet later advised us to try a list of antihistame one by one for a couple of days, and then stick to one that works for as long as the eczema remains - this strategy appeared to have work because after awhile the eczema disappears with one anti-histame. Unfortunately I forgot the name for that, but if u ask the vet (mine is castle hill veterinary ) there should be a list available.
3. Put Sardine into the diet, raw or canned. This advice comes from my violin teacher who have a collie with similar skin problem, and was advised by a dog dermatologist.
I have no way of saying whether 2 or 3 works independently, or jointly, or just one of them works. But the end result is my GSD doesn't have rashes anymore.
Hope this help.