The new picture helps a lot.
It definitely looks like it has been damaged, and it's very possible that tail rot is setting in.
If I were in your shoes, i'd make a vet appointment. If the vet determines it's necessary, they will probably just cut that part of the tail off, so that the rot doesn't spread if there is any. They can heal up quite well from that.
But to me, based off the picture, it definitely looks discolored, almost like it has a hint of green growing on it? Or is that just the picture.
I'll ask someone else to chime in and give their thoughts, but those are mine.
-Brandon