'develop fever' is correct and usable in written English.
For example, you can use it in a sentence like "The patient developed fever soon after their symptoms began."
Infected persons develop fever, severe headaches and muscle aches, and loss of appetite.
Patients — most of them women — taking quinine for leg cramps would suddenly develop fever, hypotension and blood abnormalities.
Cattle develop fever and virus-filled blisters in their mouths, lose their appetites, lose weight and produce less milk.
Patients typically develop fever and fatigue, then progress to seizures, delirium, and bleeding from the eyes, nose and mouth.
The new vaccine causes some children to develop fever, which might deter parents from bringing their children back for other important vaccinations.
Students who develop fever or respiratory symptoms in the 10 days following exposure to a SARS case should seek medical attention and be isolated from others at home.
Oral ibuprofen is commonly used in hospitals to treat adult patients who develop fevers during hospitalization.
He developed fever, jaundice, and abdominal rigidity.
A 43-year-old Japanese man developed fever, headache, and diarrhea in August 2010, while in Sri Lanka.
Two years earlier, in 2007, the patient had developed fever, skin rashes, nausea, breathing difficulty, polyarthralgias and myalgias.
However, on postoperative day 12, he developed fever and distributive shock.
