i personally wouldn't run the half marathon, but that's just me....if you continue it will get worse and worse and possibly end up in a more serious microfracture. i have had them since high school basketball, and still occasionally get them at 27 when playing alot of ball. the only way to get better is TIME off from what's causing the injury....once healed there are things to try and prevent them such as weight training, proper warm up and then stretching in that order is huge, and also good shoes with proper insoles due to the pronation of your feet one way or another.
you said you are not a runner, make sure you are landing on the mid-foot to front of the foot area in your strides, do not run heel to toe in your strides as this is incorrect. if you try to run outside in bare feet, i promise you wont do it very long heel to toe.
ice and ibuprofen can only get you so far, but are a good aide in recovery, good luck with whatever you decide to do.
i have tried to play basketball for an entire season through shin splints, i start the season able to dunk with ease, and by the end of the season it hurts so bad i can barely touch the rim, and hurts every step.....to me basketball was worth the pain and long recovery, i guess you have to decide if the marathon is worth that or not!
oh also, some compression leg wraps for your shins help a little, i love them, but it's no miracle cure and they are expensive