In regards to immunosuppresants yes that is correct they all suppress the immune system but in different pathways. They all have different mechanism of lower immune activity.
In regards to eczema not being a auto-immune disease you are wrong. do your research and read the latest medical research papers which have confirmed eczema is indeed a autoimmune disease.
eczema can effect the body in any area and can effect lots of area or small areas. The symptoms of eczema is thickening of skin, crusty/flacky skin, red/irritated skin, swollen/inflammation, high tendencies of secondary infections. we have all these symptoms.