Where does a kidney infection hurt?

Pyelonephritis: Infection within the kidney causes flank pain. The sepsis syndrome that accompanies this can make patients feel achy all over.

Two reasons: 1) just like infections that you get on your skin (large zit, abscess, ingrown nail), the resulting response will cause inflammation in and around the organ. The inflammation also results in swelling. 2) since the kidney is surrounded by a tough membrane called the capsule, swelling increasing the pressure in the kidney, which can also register as pain.