Periductal mastitis (PDM) (also called Zuska’s Disease or subareolar abscess) can occur in the setting of breastfeeding, but is not a result or complication of breastfeeding. Treatment includes smoking cessation and kenalog injection into the lesion to treat chronic inflammation.
It’s not very common, but men can get periductal mastitis as well. Here’s an example below that needed drainage and antibiotics to resolve.