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I am sorry to hear you are worried about Alex. My name is Rebecca. I am a veterinarian and will do my best to help.
How long has this lump been there? It sounds like it is either an infection, or it could be a growth/tumor that has become infected.
I would keep the pus cleaned away, and try applying warm compresses to help draw any more infection from inside. If this is all infection, once it has drained, it should seal over and heal. If it keeps draining, he may need antibiotics.
If you are worried about the lump being more than an infection, your veterinarian could do FNA, fine needle aspiration, where a small needle is used to get a sample from the lump to be sure it is not cancer. Possibly your vet could also just look a the draining fluid microscopically as well.
Let me know if I can help with or answer any other of your questions.
How is Alex doing? I hope you were able to read what I sent. Rebecca