Shin splints is a generic term for any pain in the lower leg, but it sounds like that is what you may be suffering from. Have you been fitted for running shoes at your local running specialty store?
Many times these issues can resolve if you wear proper shoes for your pronation, slow down, be careful not to add more than 10% to your run distance and intensity, ice your shins and do some stretches and strengthening exercises such as towel scrunches, the alphabet stretch (you trace the alphabet with your feet while sitting in a chair with your leg extended in front of you, calve raises, etc).
I wish you well!
HAPPY SPARK RUNNING!