Not sure on the peroxide because can't it cause tissue breakdown? I'm sure once is fine though. Are you wrapping his paw after you put neosporin on it or are you using an e-collar?
It is hard and mushy but what color is it? Can you see through it? Is there pus in it? Callouses wouldn't be that irritating I wouldn't think. If it isn't getting noticeable better, I would let the vet look.
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