I was suffering from eczema for about 7 months, which means that I really know how uncomfortable it can be and how it affects your everyday life. Although I didn’t have a very serious case, I had it on three of my fingers on my right hand, which means I had to be careful all the time to prevent any infections.
From what I found it’s called dyshidrotic eczema, or simply dyshidrosis. Some sources also refer to it as pompholyx. Of course it didn’t look very nice so I also used to simply kind of hide my fingers in the public when it was possible.