It sounds like the most likely cause of the symptoms you describe are in fact simply whiteheads. Whiteheads are a form of acne
that can occur when the skin pores become closed off and obstructed due to an accumulation of dead skin and other debris. This allows skin oils and other material to build up behind the obstruction, causing the "whitehead."
Generally, you should avoid squeezing whiteheads, as they tend to become irritated and infected when they are squeezed. What you can do, on the other hand, is scrub them gently with a luffa or use an exfoliating body wash to try to clean out the material that is clogging up the pores.
Alternatively, if the 'bumps' are much larger than an average whitehead and occasionally become inflamed and enlarged, then this might be an epidermal inclusion cyst, which is very common as well. Again, squeezing of the cysts should be avoided. Sometimes cysts can become infected, which can require the use of antibiotics and, if the infection recurs, removal of the cyst itself.
If simple hygiene and skin exfoliation do not clear this issue up for you, then you should talk to your dermatologist
or primary care doctor
to see if anything further should be done.