The indefinite article is necessary with "fever". The use (or non-use) of the article with medical conditions is one of those things that just has to be learnt, as you can see from the following list:
I have a fever.
I have a cold.
I have [the] flu. AmE: I have the flu.
I have [the] mumps.
I have German measles. AmE: Also, I have [the] measles. (to my best recollection)
I have chicken pox. AmE: Same, but chickenpox is one word.
I have tonsilitis.
I have laryngitis.
I have a headache.
I have earache. AmE: I have an earache.
I have backache. AmE: I have a backache.