Not a teacher, nor a native.
The OALD says that 'fever' can be both countable and uncountable in the meaning of a medical condition in which a person has a temperature that is higer than normal.
But there is no example where it is uncountable.
The collocations section gives a few more examples:
to have a high temperature (BrE)
to have a fever (AmE)
So I guess the indefinite article can't be leave out here.
Let's see what teachers say.
Student or Learner