This seems more appropriate for the dermatology forum. I don't believe an std shows up below the belly button even if it goes down as far as your penis.
I think that it would be more accurate to say ...."when opened"...instead of using the word "popped". They don't really "pop" like a zit does.
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. People who don't happen to have MC in childhood sometimes get it as adults, typically in the genital area, lower abdomen, etc. It often is sexually acquired, but there is some debate about that; most cases probably are sexually transmitted, but not all. There are several potential treatments--freezing, simply scraping them off (not as painful as it sounds), imiquimod (Aldara), and other options.
Put aside your hesitancy and get examined to learn for sure what you have and get advice about treatment. Your recent sex partner(s) need to be checked and, if you have MC, you need to be checked for other STDs.
I am at a loss to imagine a profession that requires medical status monitoring as a condition of employment or where one's medical records are an open book, assuming you are in the US or other non-dictatorial country. The military comes closest, but even there it is only a privacy issue. In the US, it is absolutely illegal for any such health care provider to share your medical information with your employer or anyone else, without your permission--even if the health services are provided by the employer. In any case, I don't buy the excuse and you need to see a professional. If you don't want to visit your primary provider, go to one not part of your employer's health care system or to your local health department STD clinic.
Good luck-- HHH, MD