Shin splints are actually best thought of as stress injuries (microscopic) of the bone in the lower leg and ankle area. This micro-injury leads to local swelling of the surrounding tissues and localized pain. Shin splints can actually progress and become a stress fracture if ignored. Fortunately for most people, this does not happen.
The best plan for dealing with shin splints is to continue your valuable exercise program, but perhaps hold back the intensity or duration for a few weeks. Also, try icing the affected area for 10-15 mins after your activity. In a couple of weeks, all should be better and then you can usually push forward with your training program.
If your pain persists beyond this period of time, see your physician.