My daughter had a similar sounding situation. I can't remember what the pediatrician called it but he did warn it was difficult to get rid of. He actually prescribed aldara (which was embarassing for me to get b/c he told me it was prescribed for vaginal warts!). It worked great, it dries them up over a few applications to where it is almost "scabby" and flakes off. Can be a little uncomfortable because of the drying effects so maybe work on a few spots at a time. He also told me it was contagious but I touched them on my daughter and never caught them. Basically they come from an internal type virus. This was what my daughter had, maybe you can run it by your Dr.
It can be molluscum contagiosum as it is the commonest cause of bumps in school age children. Molluscum contagiosum is a common, benign, self limiting viral infection of the skin. It generally affects children and typically occurs in the 2-5 age group. Treatment includes physical destruction or manual extrusion of the lesions, cryotherapy, and curettage.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.