It is plausible but by no means established that antipyretics (fever suppressors) in particular could increase the duration of infection/symptoms, because fever is part of a functional immune response.
From Graham et al 1990 (a small [n=56] randomized trial of the use of antipyretic pain relievers in volunteers experimentally infected with rhinovirus):
Deep lacerations of the scalp that penetrate the fourth layer (area of loose connective tissue) have an increased risk of infection. This is because pus and blood spread easily within it. This can easily pass into the cranial cavity along the emissary veins Therefore, infection can spread from the scalp to the meninges and could lead to meningitis.