PLEASE get fitted for your running shoes. Shin splints can be caused from wearing the wrong shoes but they can also be caused from doing too much, too soon, running hills, etc.
This is one reason why we need time for our body to adapt to the demands of running. The last system to develop fully in a runner is their musculo-skeletal system (bones, muscles, connective tissue, etc).
I would suggest you get fitted at a running specialty store, ice your shins, do some nice exercise to strengthen and develop your anterior and posterior tibialis muscles.
Sit in a chair with your leg extended in front of you. Trace the alphabet in cursive with your toes trying not to break the rhythm. Do this on each leg 3-5 times, 2-3 times a day.
Put marbles on the floor and pick them up with your toes and place in a cup. Do this 1-2 times daily with each foot.
Place a towel flat on a wood/tile floor. Sit in a chair and then use your toes to scrunch the towel in a heap. Do once on each foot daily.
Fill a tube sock with gravel or coins (that you find on your walk/runs....LOL), seal with rubber band. Sit down and drape the sock with the coins or gravel equally distributed over your foot....then lift your foot toward the ceiling. Do this 10 times each foot several times a day.
You do not have to do all these exercises, I just gave several options, but you will want to do these to help strengthen the lower leg. www.sparkpeople.com/resource/fitness_artic
I hope this helps!
HAPPY SPARK RUNNING!