I would get in and ask for some blood work to be done, plus a UA.
I think they are betting that the fever is viral.
Went through the same w/ my daughter around that age and I finally was exhausted from the illness, worry, dr. visits, etc. and insisted they "DO SOMETHING!"
She was hospitalized for +week for septicemia -
I was told by the dr. the up and down fever is typical of viral, along with the behaviour you described. (ok during lower temp, fussy during high temp)
My daughter's fever would spike 105 F.
(Pre hosp., tyl + motrin would bring down to 101F.)
A simple blood test a few days into this probably could have avoided the long hospitalization and severe illness she suffered. She was "touch and go" for awhile. Very scary. I did not leave the hosp for the entire time she was in.
Granted, this is the "zebra" but I think parents have to follow their gut and ask for tests if they don't think things are progressing.
It is the ins. companies that hold the doctors back from doing them.