Bumps on the skin of the pubic area or shaft of the penis could be ingrown hairs. These occur when the hairs curl back on themselves and grow back into the follicle, causing a red, raised bump at the base of the hair. Similarly, folliculitis is an infection of the base of the hair shaft, caused when bacteria get into the hair follicle. Both conditions may 'pop' when squeezed, and they are both associated with friction and shaving. Antibacterial ointment and gentle exfoliation may help, however if there are any large, painful areas you may want your primary care doctor
to look at them. Avoid squeezing, as this may just lead to infection.
Sexually transmitted infections that can cause bumps on the shaft include herpes, which usually causes painful blisters with clear fluid in them that may pop to yield small slowly healing ulcers. Genital warts
cause larger, fleshy, soft growths of skin that are painless. It does not sound like you have either herpes or genital warts but, as always, if you have any concerns that you might have a sexually transmitted infection, this is something you should talk to your primary care doctor about right away.