The pain that manifests itself as shin splints can come from different sources, but most commonly it's tendonitis. Take a few days off, ice your shins, and take some NSAID until the inflammation goes down.
Go to a reputable running store or a PT and get a gait analysis and some recommended shoes.
When you start back running, start slowly. No more than 30 minutes every other day. Stick to firm surfaces and keep the pace mellow. Packed trails are fine, but the beach is not. If you want additional endurance exercise, swim, bike, or hit the elliptical. After 2-3 weeks of this, you can increase your volume, no more than 10% per week. As you increase volume, you can run on consecutive days if you want, but keep it to 2 on, 1 off for another 3 weeks or so.
Hopefully by then your lower legs will have adapted and you can increase volume again if you want, but try to keep it to no more than 10% per week.