The pain is the symptom rather than the problem. In my experience, people who get heel pain like this often have core related issues, which causes impact problems on the ground. Splints do not solve the problem, they stretch the tissues.
Usually, people who get heel pain overpronate on the opposite side and on the same side of the pain the quads, psoas and other tissues that flex the hip tighten, and on the other side the back of the leg tightens as well. This shortens your stride and eventually will cause your core to tighten up and distort.
Basically, the problem is caused by the distribution of force. If the problem is chronic, it is possible to have a stress fracture but that is less probable. See a good sports certified chiropractor to get some good treatment and advice. My book, Cheating Mother Nature, what you need to know to beat chronic pain (available on Amazon.com) may be a good read for you since it can give you some guidance on who do see, why its happening and where to go.
I hope that helps.