Based on the history of presence of fever
and night sweats
followed by lumps in the neck the suspicion of infectious process is the first possibility. Lymphomas can also have features that you are describing that is painless rapidly growing rubbery nodes with fever.
In either case the PET scan or for that matter the CT or MRI
should have picked up the disease easily. It is very unlikely to miss a 2-3cm lesion on the imaging.
Your blood tests were also normal.
I have a hunch that these could just be lipomas
(benign fat tissue swellings ) that you did not notice prior to this. But they do not grow at the rate you are describing.
The best course would be to take a biopsy
and check with the results.