"Shin splint" is a very generic term for what could be anything from muscle pain to stress fractures. It's true medical name is Medial Tibial Stress Syndrome. I know it well.
Having proper shoes is critical. Having a pro at a running store fit you is imperative. They will watch you run, and place you in a shoe to address your tendencies (pronate, supinate, neutral).
Staying off concrete and other hard surfaces is imperative. The extra pounding is a major contributer to the problem.
Stay flat. Uphill and downhill running probably hurts more. Like the brakes in your car, you'll really notice pain on the downhills.
Practice R.I.C.E. The ice part always helped me a lot. I also used ibuprofen.
If you are cautious, you can keep training. Make sure you have the best shoes, and or see an orthopedist. The shoes make all the difference in the world. Don't wait to find this out...
I put a link to a decent site that talks about shin splints.
Good luck!