Is it possible to have pyelonephritis and only feel flank or costovertebral angle pain without high fever for a long time?

Unlikely: Most back pain, even pain that is in the upper back and on one side, is of musculoskeletal origin. In the absence of fever or cloudy urine, infection would be unlikely. Kidney pain without infection is most commonly caused by obstruction to the flow of urine as can occur with kidney stones. There are a variety of rarer causes of flank pain, so see your doctor if it doesn't subside.