I’m sorry to hear that your fellow has paw pads that are cracked, inflamed and bleeding when he cleans them.
I understand that antibiotic therapy was helpful, but the lesions have returned now that he is off them.
Certainly a food allergy can cause itchy feet and excess grooming of the feet and if he grooms enough that could lead to a secondary skin infection. Usually with food allergies though we see other areas (the ears, face and abdomen) also affected, not just the paws.
If he doesn’t go outside trauma is less likely, although this can be from a burn if he’s a cat that likes to get up on your kitchen counters.
Another possibility is an autoimmune disease (body attacks itself) such as plasma cell pododermatitis, pemphigus or vasculitis (inflammation of the small blood vessels) that has led to erosions and ulcers of the skin of his pads.
These diseases are diagnosed via a biopsy at his veterinarian.
Treatment will depend upon the particular disease but usually involves immunosuppressive doses of steroids and antibiotics to treat any secondary infections.
Plasma Cell Pododermatitis is also somewhat responsive to the use of Doxycycline, an antibiotic that also has anti-inflammatory properties.
Below is a link to a picture of a cat’s paws affected by pemphigus foliaceus. The lesions tend to affect multiple paw pads, and have a proliferative, “crusty”appearance:
And below is a picture of a cat with plasma cell pododermatitis. The lesions can affect one paw pad or several at a time, give the pad a “pillow” appearance, and a more dry and cracked than a proliferative appearance:
I would have him rechecked by his veterinarian.
In the meantime try to keep his feet clean, especially after trips to the litter box. You can soak his affected feet in a dilute solution of warm water and antibacterial hand soap and then rinse in cool water and pat the paws dry.
You may also wish to start an omega 3 fatty acid supplement as these are natural anti-inflammatories and improve skin health in general. I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give him 20mg of EPA per pound of body weight per day. For example an 8 pound cat could take 160mg of EPA per day.
Rarely we can see skin lesions due to a upper respiratory virus, particularly the Herpes virus. That would be less likely if he has not had any symptoms of sneezing, eye or nasal discharge.
I think that it would be prudent to check him for immunosuppressive viruses, (feline leukemia virus and feline immunodeficiency virus), since his symptoms have lingered. A simple blood test at his veterinarian’s office can be done.
A biopsy of his affected paws could be very helpful in determining a treatment plan as well.
Please let me know if you have any questions.