From your description, it sounds like your cat has sores on the nose and several toes. Potential causes include fungal skin infection (cryptococcus, sporotrichosis, less likely ringworm if the lesions are ulcerated), an unusual bacterial infection such as Actinomycosis, nocardia, or mycobacterial infection, an autoimmune disease such as pemphigus, or multifocal squamous cell carcinoma (a type of skin cancer). The partial/temporary improvement with antibiotics suggests a secondary staph bacterial infection is present, but the underlying cause needs to be found. If the skin culture is not elucidating, then I recommend evaluation by a veterinary dermatologist for biopsies; there are several not too far from you:
Kathy C. Tater Phone: 617 524-5733
Angell Memorial Animal Hospital - Boston
Angell Dermatology Service
350 S. Huntington Ave.
Boston MA, 02130 Hours:Tuesday-Friday 7:30 am-5:00 pm
Gene H. Nesbitt DVM, DACVD Phone: 508-393-8339
VCA Northboro Animal Hospital
286 West Main St.
Northboro MA, 01532 Hours:By appointment
Laurie J. Stewart Phone: 978 399-0100
Veterinary Dermatology of New England, Inc.
25 Carlisle Road
Westford MA, 01886
Kimberly Coyner, DVM DACVD
Dermatology Clinic for Animals of Las Vegas