Thank you. This does help.
Welcome to the HIV forum.
You can relax. Your estimate that the risk is "probably slim" greatly overstates the risk. There is no risk at all, assuming you are in the US or other industrialized country -- and probably no risk even if you are in a location where HIV is common in children. In industrialized countries, the likelihood any particular child has HIV is near zero; there are only a handful of such kids in the entire United States. And even if the blood were HIV infected, such brief fleeing contact is nil. HIV is not transmitted by contact with intact skin, and even a wound has no effect unless it is deep, fresh, and bleeding. Your hagnail makes no significant difference.
Really, don't worry about this. Avoid high risk unprotected sex, and avoid injecting drugs with shared equipment. If you do these things, you will never, ever catch HIV.
I hope this helps. Best wishes-- HHH, MD