This could be an allergic reaction to the hot water, allergies are common in people with a history of eczema.
A physical urticaria is a skin rash brought on by a hypersensitive reaction to body heat. Symptoms follow any stimulus to sweat such as exercise , heat from the sun (which could also indicate solar urticaria), saunas, hot showers .
The affected area will often feel warm and can be extremely itchy or exhibit a burning sensation. Typically the rash occurs on the upper trunk and the arms but can appear on other parts of the body.
There is some evidence that in at least some individuals the condition is hereditary.THe treatment is with antihistamines such as loratadine (Claritin), hydroxyzine, cetirizine.
However they are not indicated in your case since they go away, which is quite typical of this condition.