Hello and welcome to healthcaremagic
Dry, red, scaly, itchy and at times oozy patches are a common presentation in those who are atopic/allergic. The underlying cause is
dry skin as a result of low water retentive capacity of the skin. There is usually a familial history of atopy like
rhinitis,
asthma, recurrent cold, dry skin etc
Repeated hand washing with soaps/detergents and hand sanitizers etc worsens the condition.
If I was the treating doctor I would have advised a course of an oral antibiotic for a week, to let the oozing and discharge subside. Simultaneously, you could apply a
topical steroid + antibiotic ointment, twice daily over the scaly itchy patches.
A good/intensive moisturizer is a must for them because it would keep the skin hydrated and prevent future development of these eczematous patches. Moisturizer should be applied frequently, and after every hand wash.
An OTC antihistamine e.g
cetrizine would help symptomatically.
regards