The ring worm on my hand seems to not go away. but if the ring worm is gone could it be eczema that took its place.it itches like crazy. & with heat?

Possibly: It could even have been eczema from the beginning; sometimes they're hard to tell apart. Make sure you're using hypoallergenic skin cleansers and lotions, and if you've already used a fungal cream 3 times daily for 2 weeks without improvement, stop that and start Hydrocortisone 1% ointment 2 times daily. If not improving after a few days, please see your doctor soon.

Yes.: You could have a contact allergy to the topical medication you use for treating the ringworm.