Can anybody identify these spots/bumps?

[janepipe]

DS has had about a dozen appearing over the course of about 10 days. They don’t seem to be itchy or sore but are raised and quite large I think.
We have brand new mattresses so scary bed bugs are ruled out…and I’ve not made any significant changes to washing clothing etc.
Please put my mind at ease…

They look like they could be molloscum. (I think that's spelt right).
My DD had it especially under her arms. It's contagious, I think she caught it from using shared armbands at swimming.

I'm afraid they last for ages (months and months), but don't hurt and one day suddenly disappear, like the body suddenly realises how to get rid of them!