What is the cause of ankle pain (outside) after a run? and how do i fix it?

Stress fracture: Maybe it is a simple sprain, but it is possible that you may have a stress fracture from the repeated trauma (pounding on your ankles as you run). Take it easy for couple of weeks along with motrin/aleve trial. Do good range of motion/stretching, and use a new/good pair of running shoes. If not better, consult doc for an eval. Good luck.

Sprain : Ice, rest, more supportive shoes. If swollen or pain continues see physician.

Could be : A sprained ligament or peroneal tendonitis. Ice is helpful, you may be better off wearing an ankle brace while running until this pain subsides. An antiinflammatory can be considered as well.