You'd think I would have done this to myself at least once by now, but nope. It's not a serious burn, just red, but it stings. :/
It should pass fairly quickly (I managed to accidentally burn the tip of the ring finger of my left hand yesterday by touching a very VERY hot piece of copper strapping that I was silver-brazing it to another piece of copper strapping.) Pain is now gone but I'm still aware of the injury, that will take a while to heal.
But if it's bothering you apply an ointment as needed that has a high concentration of one of the "caines" in it [benzocaine, lidocaine or cocaine (OK, that last one can't be had OTC, but it's damned effective as a topical).