I used to have shin splints when I played soccer in high school and my coach told me that it was b/c of my cleats, at the time I had just purchased them, so I had to get new one's that supported my foot better. Once I did so the pain went away. I know you said that your shoes had less then 50 miles on them but there's a possiblity that they don't have enough or too little support, control, or they just may not be the right shoe for you. You should go to your local running store and they may be able to help you solve your problem.