Periductal mastitis: This condition is characterized by inflammation of the ducts under the nipple, often leading to a bump and drainage. It's a common cause of nipple discharge and is more frequently seen in smokers.

Ductal ectasia: A condition where the milk ducts in the breast become widened, leading to a bump and potential discharge. It's often associated with periductal mastitis.
Intraductal papilloma: A small, benign tumor that grows in the milk ducts of the breast. It can cause a bump and nipple discharge, especially if it's located close to the nipple.
Breast abscess: An infection that causes a pocket of pus to form in the breast tissue, which can lead to a bump and drainage. It's more common in lactating women but can occur in anyone.

Breast cancer: Although less common, breast cancer can present with a nipple bump and discharge, especially if it involves the ducts. Inflammatory breast cancer, for example, can cause skin changes and nipple retraction or discharge.
Paget's disease of the breast: A rare form of breast cancer that affects the skin of the nipple and, sometimes, the areola. It can cause eczema-like changes, a bump, and potentially discharge.

Tuberculosis of the breast: A rare condition where tuberculosis infects the breast tissue, potentially causing a bump, drainage, and other systemic symptoms.
Syphilis: In its secondary stage, syphilis can cause a wide range of skin symptoms, including rashes and lesions that might resemble a bump on the nipple, though this would be extremely rare and part of a broader symptom complex.
Fungal infections: Certain fungal infections, like candidiasis, can cause skin changes and potentially a bump or drainage around the nipple, especially in immunocompromised individuals or those with a history of breastfeeding.