I mean receiving care is a good thing, it often helps to relax the recipient and of course happiness hormones are good for Recovery too.
But yeah otherwise this is a overreaction, probably giving the author a chance to let them fuss over the MC.
Getting some fever suppression when you're near 40°C isn't that wrong though, since you do want the fever to fight the infection, but it should not cross that magic line or you're the one that gets destroyed.
It seems that in Manga/Anime they get fever suppression medicine, no matter how strong the fever is. I don't know how true that is to their real culture.
Also calling a difference between the flu and a cold during the early stage is often times impossible, unless you would run intensive tests. so I doubt that the doctor had any opinions on that since the illness just started.
Alright, real world rant over.