My daughter scratches when she sweats, too. I know that there different kinds of eczema (ie, dry, oozing, etc) and that different kinds are treated with different remedies.
My daughter was on Sulphur. She's taken a few doses over the course of the last few months. She also took something called Calcarea carbonica, but that was very recently.
I think if you want to try homeopathy, you've got to try to find a good classically trained Homeopath in your area.
John Stanton, on that other board, took our case and helped me entirely through email. I took a huge chance, taking advice like that, but it worked out perfectly and he took a lot of time to understand my daughter's case before he suggested a remedy. Some days we emailed back and forth 20 times. It was very time consuming.
But, as you read, my daughter's eczema is gone, so the chance I took paid off well.
Let me know if you want or need any other information.
I'm so glad to hear that your daughter is doing so much better, too. I wanted to follow Donia's advice, but the supplements she suggested contained corn and that's the only thing that we're trying to continue to avoid for my daughter. I'm glad it's worked out for you, though. :)