Getting the proper walking/running shoes is vital to prevent shin splints. First you should rest, your body has to recover, and ice your shins most importantly. You need to get shoes that support the arch of your foot.
Has your Dr. diagnosed it as shin splints or are you assuming it is?
If it is shin splints, rest is number 1!! Also Ice every few hours and take an anti inflammatory. Also physical therapy helps. when you get back to your regular workout start easy and make it short. Check with your Dr. first.