When you are allergic to something your skin my react in a way so that you develop a rash/hives. A more common diagnoses is acne. Acne forms on your hands and arms from bacteria and oil glands.
Psoriasis may cause red patches on skin. This occurs because skin cells turn over much faster than the usual 4 weeks and build up to form the red patches. Psoriasis occurs commonly on elbows, hands, knees, scalp and back.
There are a number of things that cause red sores to appear on my hands and arms. The most common reason is an allergic reaction to something in the environment. However, it can also happen if I have been out in extreme heat.