Sounds like you might have molluscum
contagiosum. The location is typical. When expressed, there usually isn't pus, but a solid white core, followed by bleeding. If you look closely (e.g. with a magnifying glass) and you see that some of the lesions are pink, a little shiny, or have a dimpled center, that's for sure what it is.
MC is primarily an infection of young children, who get lesions mostly of the face, transmitted by contact with other kids' saliva, e.g. in day care.