Shin splints are tough no doubt. You might have some success also with trying a couple of things:
1) using your hands, compress the tibia and fibula halfway down your shin. In this manner you will be squeezing the bones together. THIS IS NOT A TOURNAQUET! You are merely pushing on the sides of the calf to push the bones together. The blood flow will and should be intact and undisturbed. You don't have to use a lot of force. Compress for a few seconds at a time followed by a rest period. If this creates some relief, then you may need to find an orthopedic device that will do it for you. The good thing about this device is that it can be worn either while you run or afterwards to treat/prevent the pain. This method is assuming there is lack of normal approximation of the tibia and fibula in running gait. This is evidenced by the fact that not as many people who had their fibula surgically removed suffer shin splints.
2) Lie flat on table or furniture and have someone pull your feet towards them as they stand at your feet. During this manuver you try and resist with your feet while they are pulling down. This action will usually shift the talus posterior where is should normally be. Running can easily displace the talus anterior. An anterior talus bone can often create gait imbalance for the muscles holding tibia and fibula together.
In both cases, if the pain persists then you need to see your doctor for a referral to an orthopedist or physical therapist for treatment. However, a good sports chiropractor can adjust your foot and leg bones and usually alleviate the problem for longer periods of time.