A form of eczema seems most likely. I suggest using any form of hydrocortisone available to you, plus lubrication with any moisturizer. Chances are the rash will diminish or go away in a week or 10 days more. If it doesn't, or if it spreads, I'd seek medical attention, only I don't think you'll have to.
Best.
Dr. Rockoff
Do you drink a lot of coffee? I used to have something similar along the outer edges of the backs of my hands. Once I figured out it was related to coffee consumption I stopped drinking coffee and they went away.
About two years ago I went on vacation to London and Paris and came back with a similar rash that mainly affected my fingers, wrists, ankles and feet. It turns out I contracted scabies, which is a contagious skin condition caused by a mite. It's really easy to pick up while traveling from bed sheets, airplane seats, etc. The treatment is a cream that you apply from head to toe for one to two nights to kill the mites. I would definitely get it checked out because if it is scabies, it's really easy to spread to others.
If it only affects the hands and came on rapidly, it does not sound like scabies. Scabies is not easy to pick up from bed sheets and airplane seats.
Dr. Rockoff