My doctor diagnosed me with eczema, but he just looked at my skin through this magnifier, is that a correct diagnosis?

See Dermatologist: It is hard or impossible to confirm your doctors diagnosis without examining you. If you want a second opinion try to see a Dermatologist.

Often is: The various forms of eczema are often diagnosed based on the history you provide a doctor and the appearance of your skins. It is less common that it requires skin scraping and/or biopsies. Sometimes if the diagnosis is more uncertain these tests and/or laboratory(blood testing) may be completed, but again, this is uncommon for eczema. Hope this helps.

Eczema: most skin problems are diagnosed clinically through a complete history, physical exam (not just the skin), and to a lesser degree testing. Eczema(also called dermatitis) is very common, especially and presents many different ways and from different causes. By definition all typically having itching and most respond to topical steroids. If not getting better you may have it looked at again.