It can not be high/low according to my understanding.
Fever is fever.
He is suffering from fever of high temperature.
He is suffering from high fever.
"Fever is not fever" any more than "depression is depression."
One can suffer from mild, moderate or severe depression, episodic depression, etc.
With the ranges being disputed, fever can be low grade (usually between 99.9° to 101.4°), fever (101.5° - 104.5°), high fever (104°.6° - 106.4°) and hyperpyrexia - 106.5° and above, treated as a medical emergency. The only reason that it's hyperpyrexia instead of very high fever is because, well, writing very high fever as an admission diagnosis doesn't fly. If it's caused by a drug reaction or certain diseases, it's called malignant hyperthermia.
Rest assured that doctors respect these differences. Blood cultures are taken for high fever (lower if in the presence of immunocompromised status), and ice packs, /"cold blankets"/ wet sheets with fans, etc. for hyperpyrexia.
Similarly, a person can have grades of low temperature, called hypothermia.
It is not wrong.
A body temperature of 98.6 F (37 C) is baseline. A fever is a higher-than-normal body temperature.
(and therefore can be known as a high fever or a high temperature)
Terms used to describe fever or fever types:
Consider these simple expressions:
running a fever/temperature
E.g. Jane can't go to school today. She's running a fever.
Outside of clinical settings, I think it's unusual to distinguish grades of fever. So it would be most correct to speak either of a fever or a high temperature in casual use. But temperature is a long word, so I suspect that people got into the habit of replacing it with fever. But the high modifier still sticks around in their mind, resulting in the redundant high fever.
This type of transformation results in many redundant phrases. It's very common when one of the words is an acronym or initialism, as in PIN number and ATM machine.