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I am sorry to hear you are worried about your cat. My name is Rebecca. I am a veterinarian and will do my best to help.
Tylan (tylosin) would not be a good antibiotic for a bite wound abscess in a cat. We use it for chronic diarrhea, but the bacteria it is effective against are not the bacteria that cause these bite wound abscesses. I normally use amoxicillin or Clavamox for cats with draining infections, or an injection of Convenia.
I would apply warm compresses to the wound to keep it draining, and to draw the infection. Flushing the exit hole with saline solution can be helpful.
Let me know what other questions you have.
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How is your cat doing?