First of all, ask your mom to take you to a new doctor. There have been some prescription medications that have come out in the last couple of years which can help with skin issues such as eczema.
Magickally speaking, Reiki treatment could help. So could working with the goddesses Isis and Hygea, and the gods Dionysys and Ganesh. Although I doubt you'll find a cure in magick, you might find some lessening of the eczema and/or confidence building, especially when added to a medical treatment plan.