I've had that too, except on my fingers. Usually always from some surface I was doing pushups on.
Hurts like hell... and I know it's in a general location, but with mine, it seems that a very tiny pinprick is in the area, and sometimes it looks like a tiny dark spec is under my skin. So not quite invisible, but the problem is, entry direction. Big splinters you can tell which way they entered, and can squeeze accordingly to get it out. These tiny/nearly invisible ones, you cannot tell which direction to push, and either push in one direction and discover that hurts even more, and then push in the opposite direction to see it still hurts like hell but seems to be hurting just slightly less, maybe even getting better.
I don't know what they are. They aren't typical wood splinters, at least not for me, as they come at a time I am not around wood or construction material. So weird.