V.W.
Ditto the other responses about getting fitted. Particularly in light of the fact that you already have some issues with your feet. And you know you are prone to shin splints.
Regarding the shin splints specifically, there is a runner's rule called the 10% rule. Be sure to follow it, or you can very easily find yourself injured, and that will probably include shin splints. Do not increase your mileage more than 10% per week. Go slowly, especially in the beginning.
If you are only able to go a mile, then don't push further until you have been doing a mile for a week. Then only go to 1.1 miles. After another week, move up some more (not more than 10% though).
Your body needs time to adjust to the physical strain of impact when you run. Give it the time it needs and increase slowly.