I know for me, anytime I get shin splints is when I start increasing my speed or doing speed drills. As mentioned already, stay off that nasty concrete when possible.
Where did you get your running shoes? If you didn't go to a running shoe store and get your running gate anaylzed, I would highly recommend it. Just because you're wearing a "name brand" sneaker doesn't mean it's the right sneaker for your feet. Playing football is different from going out and running forward for so many miles.
Keep icing your shins after runs and do toe-taps and other shin stretches. Good luck and take care of your shins.