I'd go and see a Physio and get professional advice.
When you rest, how do you decide when you should start exercising again? Completely pain and symptom free?
Also, when you start back excerising again - do you ease back into it (I.e. build up slowly?) or just go back to running as often, as hard or as long as you did before?
How do you know you have 'shin splints'? Do you think it could be something else?
I got 'shin splints' and was diagnosed with it by a Physio - he said shin splints is just a term used for all sorts of injuries and is not the actual diagnosis. (what I actually had had a long name - medial tibia something or other). I started back running too quickly, built up too quickly and they came back. I was training for a marathon and my body couldn't take the increase in training. I then had a break and listened to the Physio and got better. Not had it since.
How long has this been happening to you?