I had a lot of shin problems when I started running and even wound up with a stress fracture in my shin and swore off running. Then my company started a running clinic, so I joined. They taught us a basic stretch which I'm sure you've seen runners doing, but that I had never done and it made a world of difference to me (and my shins). I'll try to describe it:

Standing in the street on your left leg with your left toes pointing straight at the curb, put the ball of your right foot on the top of the curb (right on the edge/angle), and let your heel fall down toward, but not touching, the street (so put your foot high enough on the curb so your heel naturally doesn't touch the ground). Your right foot will be more vertical than horizontal. Keeping your right leg straight, bend forward (towards the curb) at the waist. You will probably feel this stretching your hamstring. Hold for 30 seconds, then switch legs.

At first, I always bent my right knee when I did this stretch because I could feel it stretching my shin that way, but the trick is to stretch the hamstring so your shin doesn't get pulled so much while you run.

I hope that was helpful. It's something that really helped me a lot.

Good luck! Jenn