Sorry I was off line earlier, does your employer stipulate that the fever-free period must be without use of antipyretics?
What is your job?
Have you been assessed for any other possible causes of your fever such as urinary tract or ear infection?
You do need to ensure that you are adequately hydrated, as dehydration secondary to fever is a common cause of headache.
Antipyretic is any drug that reduces temperature in fever so that includes tylenol, ibuprofen and aspirin.
I would suggest that you have 24 hours with plenty of fever, rest and appropriate doses of tylenol or ibuprofen then reassess your fever.
At the moment we do not know how the fever will respond, I would expect most self limiting illnesses to respond quickly to the medication and you should be ready to return to work in 48 hours. If the fever is not controlled by medication, or returns to a high level after stopping the medication then you should see a doctor for a respiratory examination, ear and throat examination and urine analysis. I would also suggest blood tests to see if white cells are elevated as that would confirm underlying infection.
As we do not know what is causing the fever, then we do not know if you are contagious at all. If your fever was due to urinary tract infection (for example) then we would not expect this to be a risk to other people.
The tylenol will control the fever, regardless of the cause.
Bear in mind that normal body temperature includes a rise over the day and that the method of temperature measurement an affect the relevance of the temperature. For example, rectal measurement is different to armpit. Digital thermometers are more accurate than strips.