Are you sure your cat isn't weeing in the same spot? When I lived at home my mum got a kitten that scratched up a corner of the carpet in the hallway, and it turned out he'd been weeing there when nobody was looking. We never noticed the smell, because his litter tray was close by anyway.
I would say definitely try a scratching post - cats do need to scratch something - spraying it with catnip spray or rubbing the leaves on it is supposed to encourage them to use it, my cats have always used them by themselves. If your cat has a certain spot she likes to sleep in, put the post nearby as cats like to use them to stretch when they wake up. My cats have scratched up the wallpaper around their litter tray (it was in a corner), but I suppose that was to be expected as they naturally scratch around when they're doing their business. A covered tray or bare walls would have avoided that.