I'm not a runner, and thus, am not sure what effects terrain will have for your condition.
What I do know is that shin splints consist of inflammation caused by overuse.
First, I would consider another form of cardio for a while in order to rest your shins.
Next, you may wish to examine your footwear and determine if that may be a culprit.
While treating your splints, OTC NSAID's may be a good idea, as well as ice - in fact, I HIGHLY RECOMMEND ICE.
When you start running again, start light and implement a gradual progression.