I'm sorry your kitty is experiencing this problem with her claws.
From your description of the back claws that are causing her pain, it's possible that she has a fungal infection of the nail bed, called Paronychia; this is an infection that causes inflammation of the tissue around the nail or claw. Onychosis or Onychopathy are generalized terms to specify an abnormality of the nail, itself. If you see fresh or dried blood or a black discoloration, around or under the claw, these are symptoms of a nail bed infection or claw abnormality. Ringworm, a fungal skin infection is also possible in the claw beds; this is contagious to humans, too, so wear gloves when you look at her claws and wash your hands well until you can find out more after a vet visit. Here is additional information:
Older cats have thicker claws, and shed the sheaths more often; they are also more prone to breaking or splitting, due to being more brittle.
At the moment, it would be best to have your kitty's claws evaluated by a vet, so a definite diagnosis can be made and treatment given.
I hope all will be well with your furry girl!
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