There is clearly an underlying disease process that has not been found yet.  Cats can develop callouses but they should not be uncomfortable and unable to walk on their pads.  I recommend having x-rays taken to assess the foot further.  This will tell us if there is a deep bony infection (can be fungal or bacterial), screen for fractures, and bony tumors.
If the x-rays are normal it is time to sedate your cat to explore the area surgically to search for a foreign body present and take a biopsy.
Bloodwork should be run prior to anesthesia to ensure a safe anesthetic event and to make sure there is no problem with the internal organs etc that could be related.
There are veterinary dermatologists that are a great resource as well.

 The cats and dogs develop callus to protect from injury. This callus is damaged by walking on the rough surfaces in few pets. This can lead to tear in the callus which can lead to infection. The allergic reactions on the paw can cause itching so the cat can lick her paw for longer times and the paw become wet, sore and raw. Liver diseases also cause cracks in the paw and zinc deficiency is also responsible. I advise you to take your cat to vit dermatologist for proper diagnosis and treatment.

 It might be feline progressive histiocytosis. My cat has had exactly the same problem over the past 9 months (again, tried antibiotics and steroids to no avail)It could also be an autoimmune condition (this was our vet's first idea)--don't know the exact name for it, but she called it