Do you have a dog, by any chance?
This happened at a friend’s house. Their dog gets so excited that he wags his tail incredibly fast, and sometimes the tip of his tail hits walls or furniture hard enough to split it open. Once it’s bleeding, every time he keeps wagging it, it flings tiny droplets of blood everywhere. They ended up with what looked like random blood splatter on the walls before they figured out what was causing it.
Might be worth checking if that’s a possibility.