Hello and welcome to healthcaremagic
I would keep a possibility of Dry discoid
eczema. As the name suggests they are disc shaped eczematous patches on
dry skin. Tinea/
fungal infection is a close differential of dry discoid eczema but the sites are different. Dry discoid eczema tends to occur in area like outer thighs, lower legs, trunk unlike tinea which tends to occur in body folds, specially in summers
Dry discoid eczema is common in cold weather because the skin becomes dry.
Atopics, have dry skin and are the ones most commonly affected, elderly also are prone to dry discoid eczema.
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