Reading your query, irritant contact dermatitis
is a likely possibility if this is restriced to both hands and wrists.
Patch tests (usually read at 48hours and 72 hours) to a variety of chemicals (or if there is a clear trigger like rubber) can be done by Dermatologists and the trigger may be identified.
Low potent steroids
with antihistamines are useful but stronger steroids can be used if required.
I hope this was useful.