Shin splints are near and dear to my heart - too many miles (50 +) a week on mostly pavement in the wrong shoes killed me. It was the first time I have had to stop running due to an injury. Anyway, I went with the most cushioned shoe on the market for neutral runners - Nike Vomero - and in conjuction with treatment and PT - the pain is almost completely gone over the past 3 days, and getting better every day. After I get my legs used to running everday and 50-60 miles a week I will start to rotate a firmer shoe into the mix. I know Nike also makes a "Vomero" stability shoe called the Zoom Equalon 3 which has gotten great reviews.
http://www.roadrunnersports.com/rrs/products/NIK1244/ (Just mentioning both since I don't know what type of runner you are.) From my personal experience of dealing with shin splints getting the right shoe has solved the problelm. Good luck!
But back to your original question - it depends on the pain. When I first began running a couple years ago I just ran through the pain, changed shoes, and it slowly got better. You do run the risk of getting a stress fracture if it gets bad enough - so better to fix the problem.