*true* shin splints are a form of tendonitis-- medial tibial tendonitis. The correct shoes and/or inserts will "cure" it. You may have to get custom orthodics to fix it. The tendonitis wont go away on its own because its caused by a biomechanical feature of your body/legs/feet/gait wahtevver. If i remember correctly people who who supinate and/or have flat feet are more prone to shin splints. Also, learning to change your gait can have aneffect as well.
Good luck