Finger eczema is a really nasty condition. My recommendation is to not try anything that is not homeopathic, as most of the products cross the skin barrier and make you more bad then good. Avoid nail polish and rings. Use cotton-lined gloves for handling chemicals (change them often).
To wash hands, use mild soaps. Beware of bare hand contact with the vegetables and fruits. Shampoo your hair with gloves.
Finger eczema can look like one of the images bellow: