I've consciously altered my running style to avoid heel striking. I used to have pain in the outer shins (tibialis anterior) but that went away gradually. The inner shin pain has been a new development, now that I have increased my overall distance and speed.
I do run on a fairly hard surface (asphalted path in a park) and I have noticed that the pain isn't as severe when im on the treadmill.
I've cut back to running only on alternate days to prevent aggravating the pain.
Its frustrating coz Im barely out of breath when I run, but my shins give out way before my lungs do
