Buy a shoe with the right kind of support for your type of foot.
ie: if your flat-footed or high arched, choose a shoe accordingly.

Go to a shoe store where the people know their shit. Not Foot locker or someplace in the mall.

Also, Ice your shins for 15 minutes after you run.

You mentioned that your are walking now instead of running. Is this because your not used to it. If so, tough it out, and as your running improves, so will the strength of your tendons, and you'll eventually "Run it out".

I had shin splints for the first couple of months that I started seriously running. I did these three things, and now I'm fine!