I have a 6 y.o. grandaughter whos fever soared to 103.9 then disappeared after given a dose of child's tylenol (acetaminophen) which she threw up, what gives?

Fever: Fevers can go up and down quite rapidly. A fever is generated by the release of chemicals from white blood cells in response to infection. Higher body temperatures imped the growth of viruses and bacteria. Fever therefore is usually beneficial. However too much of a good thing can be harmful. Anti fever medications help lower the fever response in many ways when it gets too high.

Pretty common: Fevers with viruses go up & down on their own pattern whether you give meds or not. If they have been retained for about 30-45 minutes, you might see a degree change if the temp were sustained. If it dropped precipitously it wasn't the meds. They need hydration more than fever treatment, since fever can stimulate their system & help them heal. I prefer Ibuprofen since it lasts longer