Why does a knee that was sprain still hurt after a few weeks?

Common to still hurt: There are several grades of sprains, assuming you have been given this diagnosis. A grade ii sprain implies a partial tear of a ligament and symptoms often last for 3-8 weeks. It sounds as if you need to follow-up with your physician for additional advice, or see one for the first time if you have not been formally evaluated.

Might be more: What makes you sure that this is simply a so-called sprain? There may be more involved. Does your knee lock or catch in any specific motion or position? Does it swell up? Do you feel unstable on it? Consider seeing an orthopaedic surgeon to get a specific diagnosis and start treatment. Good luck!