Shin splints is an overuse injury. You've been running too far or too frequently for what your body is accustomed to, without enough stretching and strengthening.
Take some time off running and do non-impact workouts (swimming, cycling, water running).
As for strengthening exercises, you need to strengthen both soleus muscles, the muscles in your arches, and on the outside of your shins.
The bad news is that shin splints can take a while to recover from. I got them again for the first time in years, and after 6 weeks off running, and a lot of physio, I'm finally ready to start a walk/run program to get back into it.