Shin SPlints are often caused by a muscle imbalance between your calf (gastrocnemius, or however you spell it) and you anterior tibialis ("shin muscle"). Your calf is stronger than the ant tib. Strengthen your ant tib and the problem could go away.
You can do toe raises - pull your toe up towards your knee - thereby contracting the ant tib. You can do multiple reps throughout the day. You can also attach a band to your foot (tie it around the ball of your foot) and tie the other end to a stationary object (table leg, or have a partner hold it). The band offers resistance.