take a few of days off from exercising and rest your legs. take an anti.inflammatory med. like motrin. alternate ice and heat on your shins. make sure you are getting enough calcium and protein in your diet.
do you have a really good pair of running shoes? if not, invest in a good pair...with shock absorbers like nike. the shock absorbers cushion the heel strike. most of the impact in long-distance runners results from when the heel strikes the ground. as this happens the torso leans forward to help you keep your balance. make sure you have a running style/speed that is appropriate for you.
you can try the elliptical machine, but shin splints are not a reason to stop running...just work through it. if they do not feel betters, go see an ortho. doc.
i have osteopenia in my spine and bursitis in both of my hips...i still run appx. 50-60 miles and walk appx. 20 miles per week. i also go to the gym and lift a few days a week.
exercise can really help with pain and it obviously makes us feel good and be healthier...don.t stop