Tiny purple bump on hand (size if the head of a pin), but I don't remember an injury. Hemorrhage? Insect bite? It's painless.

Capillary. Without actually seeing the spot, it's impossible to say for sure, but it may be a ruptured capillary. No serious issue. Anticipate complete resolution in several days. If you are concerned, then getting somebody to look at it is the only way to know for sure what it is.
Likely benign. likely a hemangioma, which is benign. but, keep an eye on it. if it grows, changes color or shape, then i'd recommend going into see your doctor to make sure it's nothing serious.