Is there a remedy for itchy nipples?

Cortisone. A topical steroid can help. Rule out sensitivity to articles of clothing as a cause, either the material or laundry products.
Itchy Nipples. Nipple itch is a common symptom of allergies, inflammation, or even physical irritation, and is characterized by a tingling, irritating or uneasy sensation on the surface of the skin. It may occur in conditions that affect the nipple area itself or in association with more generalized conditions, such as hives or eczema.