My daughter has dime size red rough bump/patches on her skin....What could it be?

Eczema. This sounds like numular (coin-shaped) eczema. I would try some hydro-cortisone cream or ointment a couple of times a day. See your doctor if it persists.
Either. Without looking at it , it is hard to say.It could either be a ringworm or a nummular eczema.More than likely the latter one.A lot of times this is mistaken for a ringworm and parents have tried ofc antifungal to no avail.This need to be treated with a script of topical steroid.