Is it possible that after this drug the daughter began to have a strong fever?

You did not write what medicine you are talking about. If your question is about a tagged Avamys product, please read on. High fever is not a known side effect of Avamys and given the mechanism of action of the drug (it exerts an anti-inflammatory effect locally in the nose), in my opinion it is unlikely that this preparation could cause such a side effect. Although some extremely rare side effects may not be described, the causes of high fever should be sought first elsewhere. Persistently high body temperature in a small child should prompt you to contact your pediatrician. I enclose additional information: https://www.gdziepolek.pl/artykuly/goraczka-u-dzieci-i-niemowlat https://www.gdziepolek.pl/artykuly/czy-sterydy-sa-bezpieczne