Shin splits are usually an indication that your ankle tissues or your posterior chain (from achilles to the glutes) are tight/weak. Time to strengthen or stretch those muscles.
Zero-rise or Vibrams should help with the ankles and feet.
Calf raises should help strengthen/stretch the calves.
If you have low back pain too (or lordosis from too much sitting), then I'd focus on stretching/strengthening your glutes, hip flexors, and hamstrings. This page has some good stretches for the hips - hip /glutes/hammie stretchs.
Squats (air or barbell) and deadlifts help also, if you're so inclined.
The lower leg issues may sort themselves out in a few weeks if you perform these consistently.
In my experience, shin splints are caused by weak anterior aka front muscles of the lower leg, so I would never expect calf raises or stretches to help much there. My leg routine includes "toe curls" with a dumbbell. I lie flat on my back, legs outstretched as much as possible but still allow the toes to be put under the db handle (I use Powerblocks), and I raise the db off the floor and towards my knee, using a weight that only allows (after warmup), 15 to 21 reps.
Edit: when you first start doing this you may find that your toes, thanks to exhaustion of the muscles above, "float" lower than you're accustomed to, so be careful you don't trip going UP the stairs. : )