A boil like lesion in breast can develop for many reasons including the serious possiblities like cancer.
But in your case the most common cause; the infection is more likely.
The infection in breast are most likely to be bacterial, but the viral infection pappiloma can also give pus like exudate that is bloody mostly.
The another possibility is a cold
abcess of tuberculosis
Because the problem is persisting I would advise you to get yourself examined by a surgeon and get a histopathology and gram stain and culture from the discharge and then fine tune the treatment.