Don't know about the black spot, but don't use this kind of stuff on that part of your body -- maybe not anywhere on your body. It's basically rubbing alcohol, but whatever it was would have healed on its own most likely. But again, can't help you with the black spot.
If it was a skin tear, and you put something on it that is used as a skin antibacterial but you didn't dilute it when it was supposed to be diluted, and you left it on for several hours, it's not that surprising the edge of the tear turned a dark color. I assume it will be that way for a while and then fall off, like a scab. As Pax suggests, don't self-treat with a concentrated solution that is supposed to be diluted. See your doctor if the scab hasn't come off on its own in a week or ten days.
I agree with all of the advice you have already been given, but to add - DO NOT put anything else on your penis. Don't touch it unnecessarily. When you shower, pat it dry or allow it to air dry. Do not rub it. There is nothing you can do to make it heal faster than time alone.