Too many specific questions in your post to answer!
It's possible your shoes aren't right for you but go back and discuss with the shop who sold them. They can see your feet and your gait.
(People get shin splints for many other reasons than their shoe type)
Phys vs pod: I saw both and the pod provided orthotics. I'd start with a phys because they 'should' suggest a pod if they think it would help.........but there may be other causes of your shin splints which a phys could/should advise on