Landing on the outside of the foot and not rolling inwards enough is called "supination". A visit to a podiatrist who can make correctly fitted orthotics should sort this out. It worked for me and cured my crippling shin splints.
You will probably need to run in a neutral shoe so that the orthotic can do its stuff - Nike Air Pegasus is one recommendation, but be guided by the podiatrist.
It took a year for the podiatrist to get the right "fit" for my orthotics, but it was worth the wait.
V-rap, thanks for that. The physio did say it could be an overuse injury, confirmed by the podiatrist (who laughed when I suggested it might be a stress fracture: "If you touch it like that and it's a stress fracture, you'd be through the ceiling by now", but a relief for me).
I'll just see how it goes. It gets a bit better when I have days off (1-2 per week) but I can't imagine not running.