M.O.
I haven't had that much experience with alternative medicine (for the same reason -- the expense), but the experiences I have had have been fantastic. And something like eczema is the perfect kind of thing to take to a naturopath. They can often give you a diet to follow and that's it, so it's not the kind of thing where you have to keep going back for new prescriptions.
However, I do want to add the proviso that the world of alternative medicine is incredibly diverse, and it includes some flakes and quacks along with people with serious and extensive training. I'd recommend looking for an ND -- a doctor of naturopathic medicine.