Hi Bob,
Thanks for your question and listening to Dr. Greenway on his radio show!
First, you might want to check out the “How to Address and Where to Check for Lumps and Bumps in Dogs & Cats” video on our website. Depending on what these lumps look like on physical examination, there are a variety of possibilities here. Ultimately, some type of sampling and examination under the microscope and/or at the lab is the only way to definitively identify the lumps.
If these are indeed related to allergic disease, it is possible for them to become secondarily infected with bacteria, especially if the cat is scratching or licking at the lesions. Culturing (growing and identifying bacteria) may be needed to treat any secondary infection effectively. Your vet can guide you further on determining if this might be the case.
It sounds like you have already done a lot – figuring out what the animal is allergic to is always a challenge. Common things would be fleas (or other external parasites), environmental allergens (pollens for example) and as you mentioned, food allergies. Food allergies are the trickiest to figure out because it often requires a lot trial and error time to determine. Your vet may recommend considering referral to a veterinary dermatologist to investigate things further.
I hope this is helpful and I hope your kitty starts to feel better very soon.
Dr. Kim Hester