No, it wouldn't be athlete's foot (fungus.) There is a form of eczema called dyshidrosis which produces little bumps under the skin of the fingers. That's not very significant and usually doesn't need to be treated. I can't think of anything these could be that you need to worry about. If they persist for a month or two, show a skin doctor, just for peace of mind.
Take care.
Dr. Rockoff
When the spots on my fingertips break the surface they peel the skin and then heal. I had my doctor take a look and she said it was psoriasis. It comes and goes but seems to only affect me in the winter.
The less I worry about it the less it seems to erupt.