You are right concerning the word fièvre “fever”. These mistakes were pointed out to be corrected. I guess the editing team did not beat the clock!
However you could say J ai un rhume. or J ai le rhume. “I have a cold.” depending of the context.

Thank you for pointing out these mistakes and help learners to get these phrases correctly.

First: We never say “J’ai une fière”. It’s either “Je fais de la fièvre” or “J’ai de la fièvre”

Second: “J’ai une rhume” is an incompréhensible mistake. “Rhume” is masculin and this kind of sentence doesn’t make any sense. You cannot take a pattern (J’ai un/une..) and apply it for every situation in french. It works in english maybe, but french is more complex when it comes to sentences’ structure. So, in french we say: “J’ai le rhume”.

Third: The way “J’ai mal à la tête” was pronounced a little bit weird. It sounds as if an english-speaking guy is telling the sentence. He pronounced the letter “a” in an uncommon way. This is not the way we say it in french.

I hope those comment will help improving your lessen.