Probable fungus. If the rash is raised, reddish on the cicunference and regular skin color in the center, this sounds like "ringworm". Ringworm is not caused by a worm but is a fungal infection called tinea corporis. It is common and treatable with topical antifungals. You can try the creams used for athlete's foot or see a doctor for prescription. One source of the infection is pets. Have them checked.
Nummular Eczema. Nummular eczema is an allergy-related disorder in which itchy, coin-shaped spots or patches appear on the skin. Causes, incidence, and risk factors the cause of nummular eczema is unknown, but there usually is a personal or family history of: allergies asthma atopic dermatitis other possibilities are fungal inections and psoriasis.