Yup - it's shin splints sista! Been there, done that and it ain't fun
I agree with all the smart people above. Upping your intensity and distance is definately the culprit. Walking on incline (negative or positive) definately makes matters worse.
Back in the day (ahhh - the good 'ol days...), I used to do alot of long distance running. Shin splits hit me hard when we did any sort of hill training. Painful. Renny Sue hit the nail on the head though. You gotta stretch. I found pointing and then flexing your foot repeatedly does wonders to stretch out your shins. Make sure you feel that good stretch along the front of your leg.
Although not pleasant, I usually continued to train despite a flare up of shin splints. Seems like you can work your way through them. Often I'd have them at the start of the run, but they'd subside as I warmed up. Often I had to remind myself to put a bit more motion in my feet. Make sure I do that full "heel to toe" push off with each step. Do note though - shin splints are a sweeping pain across the front of your shin. If you can point to a very specific spot where you have intense pain - you may have a stress fracture. And running or walking agressively on a stress fracture is not recommended. You won't "work your way" through this pain. Believe me - it put the end to my running a few years ago and I still have trouble to this day. Blah! THAT you want to avoid.