A tip I got back in the 80s worked like magic for me, when I got horrendous shin splints while training for a marathon. I sat on the kitchen counter and hung a 5-lb ankle weight from the front of my foot. Then I did three repeats of 10 times lifting the weight with my toes. I did this on both legs, once or twice a day. Within 10 days my shin splints were history. Now whenever I get the slightest twinge I head to the kitchen with my ankle weight (I only have one as this is all I use it for--lost its mate years ago

).
The explanation the running book (sorry, can't remember which one it was, since it was so long ago) gave for why this works is: they claimed shin splints are caused by an imbalance in the muscles. Running builds up the calf muscles on the back of your lower leg; this toe weight-lifting works the muscles on the front of your lower leg to balance things back out. I have no idea if that's right; I just know it works for me.
ETA: Gator here, class of mumbledy-mumbledy