What might be the likely diagnosis for a young woman with bloody discharge from her nipple?

The likely diagnosis of an intraductal papilloma is supported by the symptom of bloody discharge from the nipple, particularly in young women. Intraductal papillomas are benign growths that occur within the ducts of the breast and can lead to various clinical presentations, one of the most notable being bloody or serous discharge. These growths arise due to an overgrowth of the cells lining the ducts and are often characterized by the production of blood-stained fluid.

The other conditions listed do not typically present in the same way. For instance, fibroadenomas are benign breast tumors that usually present as a palpable mass rather than with discharge. Paget's disease of the nipple primarily presents with changes in the skin of the nipple and areola, often associated with breast cancer, rather than bloody discharge. Acute mastitis is characterized more by breast pain, swelling, redness, and possible pus formation, particularly in lactating women, rather than specifically causing bloody discharge. Thus, the symptoms align most closely with intraductal papilloma, making it the most likely diagnosis in this case.