If there is pus
coming out it is an small abscess
or foruncle usually caused by staphylococcus.
All pus has to come out. Sometimes drs prescribe antibiotics to fight the infection. Some pts. Are prone to have recurrent small abscesses, like diabetics, pts. With staphylococcus in their noses, obese pts, immunosupressed other possibilities are infected sebaceous skin cysts which also require same.