They sound just like molluscum contagioseum - & the reason I know is that i've just spent the morning researching it on the net... My daughter seems to have caught them from her cousin.
They are supposedly a virus - which spread on contact - and can be gotten everywhere including the genitals and the eyes. My daughter is 10 , and her cousin is only 4 - and they both have them.
It's a common kids thing, which seems to spread like wildfire.
They say - don't burst them, don't touch them, and then touch other body parts - and there are lots of different opinions on how to fix them, including homeopathics, and to the other extreme - surgery.
You'll need to decide that for yourself.