Ooh, sounds like what I have--capillary hemangiomas (benign tumors of the capillaries; I think new capillaries start to grow unnecessarily, and they form a little clot). Children get larger ones as birthmarks--strawberry hemangiomas.
Mine are only on my hands, though. I have one "big" one on the back of my right hand, slightly raised with a sort of red area around it. I get new ones occasionally, very tiny.
Oddly enough, they don't want to bleed so much. The big one once got more raised and dry, kind of like it wanted to come off, so I picked at it, thinking it'd let out all that blood. No such luck; I think there was one drop. I told the doctor I'd done this, and it was one of the only times that I didn't get scolded when I told a doctor I'd picked at something!
Her eyebrows raised and she asked if it bled a lot.
Anyway, they're harmless. I don't know if anything can be done about them cosmetically.