Banixx is basically a scam, or at best, a normal everyday product packaged with a fancy name and with the price jacked up. Bannix is merely hydrogen peroxide in a slightly acidic solution. They say "hydronium" to make it sound fancy, but in reality, any peroxide in an acidic solution takes on a hydronium form. It is the identical product to the hydrogen peroxide you buy in the pharmacy. The "hydronium" thing isn't even special - the peroxide you buy in the pharmacy is sold in this form (e.g. slightly acidic) as the hydronium form is shelf-stable for longer than the non-hydronium form.
Long story short, Banixx is simply repackaged pharmaceutical-concentration (2.5-3%), shelf-stable (slightly acidic) hydrogen peroxide, for which they charge 2-3x the pharmacy cost because they found a big word that makes it sound fancy.
On that note, whether using over-priced and dishonestly advertised Banixx, or just regular old peroxide, you should not continue treatment for more then 5-7 days. Peroxides inhibit healing, and if the infection hasn't cleared up in that time you should see a vet (for your dog) or MD (for you) for something stronger.
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