If the pain is on the outside of the knee. . . how do these additional symtoms sound -

It doesn't hurt when you walk, but when you go for a run, after a while the pain starts and gets worse quite quickly. The pain doesn't come on footstrike, but rather its when yo flex you leg as you bring it forward for the next step.
When you stop to walk the pain quickly goes away.

If this is a match you could have ITBS Ileo-tibial band syndrome. A big tendon that goes from theoutside of your hip, down the side of your thigh and ataches to the bony knob at the top of the tibia. When the knee flexes this tendon slides normally on the outside of the knee. it is supported/slides on a couple of fluid filled sacks or bursa. These can become inflamed and are the cause of the pain. Rest, anti-inflamatories and ice will help. So to will stretching. And physio. do an internet search on ITBS

Stew