OK. These tests would be a good idea to make sure that we have a diagnosis and know what we are dealing with.
From what you describe though, I am suspicious of adult onset juvenile cellulitis. Your vet might know this as "puppy strangles". This is a sterile condition that is not caused by an infectious agent. It is treated with high doses of steroids. It is best practice to rule out infectious diseases before starting the steroid treatment, as high doses of steroids are immune suppressive and could make infectious disease worse.
I would consider switching his antibiotic from amoxicillin to Clavamox or cephalexin and then starting steroids (prednisone) right away. The steroids should be continued until resolution of the skin problems and enlarged lymph nodes, then the dose is tapered over 2-4 weeks.
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