Can changing my diet help my eczema or dermatitis?

Yes. If you know what makes it worse, avoiding these foods can make it better.
See an allergist. A better use of your money would be to see an allergist or a dermatologist. They can help determine the cause of your dermatitis.
Yes. You may be deficient in zinc, gla, ala, or dha and epa. This can be tested for with a serum zinc level (do with serum copper), and a comprehensive free fatty acid panel. Both zinc and copper should be within normal ranges but we want zinc to be slightly higher than copper.