I'd recommend stopping by a running store and get fitted out by one of the runners. They have tons of experience and will know what to get for you.
Yes, yes yes. I'm fighting shin splints right now, too, for some reason. Went out, bought a new pair of running shoes, and it did nothing (and I was doing all of the stretching, ibuprofin, etc). I was going crazy. So I finally went to one of those running shoe stores, where they look at how you run and how your foot rotates, and get a proper shoe for you. Mine has a reinforced arch, since apparently my arch falls a little too much.
It's made a world of difference. I'm still not out of the woods yet, but I can now run 15 minutes without wanting to saw my legs off at the knee. And I saw this the first time I put those shoes on. And really, at that point, I was more than ready to drop $200 on a pair of shoes if I really thought it'd help. Lesson learned, for me: 1) Go to a running shoe store where they know what they're doing, and 2) Do not chintz on the running shoes. Go to the store, try on what they recommend, pick what feels best to your shins, and pay whatever the cost is. It may the most expensive shoe, and it may their cheapest. Don't worry about it either way.