Pheidippides saidI stopped getting them after I strengthened my ankles. I have no idea what the connection was.
The muscles in the front of the leg (where most people get "shin splints") run across the ankle and attach to bones on the feet. There aren't any muscles per se at the ankle, only the tendons that run from the shin to the foot. So if you strengthen your ankle, you're actually strengthening those muscles in your leg.
Make sure you warm up and cool down, especially if you've bumped things up considerably. Stretching can help, too. Usually, you gradually increase your intensity for activities you haven't done too much of in the past, e.g. running, stair climbing, hills.
Running form can also be a culprit. Shoe wear as well. Start slow and work your way up. When you start weight lifting, you usually don't go to a 405 lb deadlift after you've only been doing 225 (I exaggerate, but you get the point). Same thing for aerobic/cardio exercise that's high impact.
If it's currently painful, rest it for a few days. ACTIVE rest, meaning do stuff like walk, or stretch, or compound strengthening exercises for the hips on down (especially hip abductors, glutes, quads, calves). I wouldn't recommend running or stair climbing right now until the pain has decreased.
The leg has an anterior and posterior compartment (and lateral, too). The anterior or front compartment houses the muscles, nerves, and blood vessels in the front of the leg, and the posterior all the stuff in the back of leg (calves and other stuff). When something swells, it takes up more space in an already squished and confined volume, squeezing other structures (thus the pain). Just "working through it" may worsen things.
NOW, if the pain is severe and/or gets worse, isn't relieved by rest, or the pain is very focused (meaning it's in one area and you can easily point to it with a finger) or just putting weight through your leg is painful, I'd see a physician.
Granted, I DON'T KNOW what you have because I'm not there to actually determine it. My advice: Go see a physician if it doesn't go away with the above "suggestions".