Hi my 2 yo child had fever ranging 39.5 to 40 degrees and paracetamol (so far given 2 rounds, 6 hr apart doesn't bring the temp down)

We are thinking if this continues until the 3rd paracetamol round and still the same we want to bring her to a hospital just in case. Meanwhile we are sponging her with room temp wet handkerchief.
Anyone done that? Does private hospital allow admission for high fever? Hope to claim insurance but need to be admitted.

Anyone have experience with avisena hospital?