Would you be able to provide an image?
At this point, a reddish rash
which involves the extremities in children suggest a likely eczematous or dermatitic condition. You have mentioned of itchiness and redness which are characteristics of both a fungal infection and a dermatitis.
Is there any associated decrease in appetite or activity? Any changes in the rash
eg discoloration, crusting, scaling ?
Is there any strong history of allergies or asthma in your family?