How big it is will tell you if it's a toothpick holder, looks as tall as a pop bottle from the pix, a little to big for a toothpick holder if it's that big. Maybe put your hand by it or tape measure for height definition to see how tall it is.
Sorry, I can't tell if it's damage or a pontil. If it's a pontil you're right, if it's fractures or a chip it's machine made. This is what I can't quite make out.