Belly button doesnt hurt..should not be washed with water. Usually people as said above get told to just gently clean it with sterile gaze and medic alchol to dry. In some country they put Tyrosur or Bivacyn powder, just to keep on safe u didnt put in some bacteria.
I doubt its her belly button. Have you noticed any change in bowel movements? Is she eating the same? Does she ball her legs up and cry? These are all things to watch would may mean different things.
check if its not that she has a fever or cant poop
her belly button doesnt hurt, it has no nerves! so moret hsn likely she is gassy or colicy.
as far as cleaning it, you can rinse it with warm water, like soak a wash cloth in the water then squeeze it out over the belly button, my pedi even gave me some alcohol pads to clean it with, it helps dry it out