As a valet I developed HORRIBLE shin splints. They can be insanely painful if you keep running with them. Short of stopping what you are doing until you are completely healed up, here is what saved me from alot of pain.
1) Lengthen your deceleration times when stopping from full speed. Your legs take enourmous amounts of force under abrupt deceleration.
2) Stretch your calves. Do this before and during activity every so often. It has the added benefit of relieving sore feet somehow if you are on them for long hours. Learn to feel when your calves are "tight" if you can't already.
3) Wear thicker socks or two of your normal socks IF your shoes can accomodate it properly. I somehow was never comfy with insoles though other valets swore by them.
4) Consciously try to land a little softer when you run. I found that landing on my heels and rolling to the front of the foot was the smoothest at speed for me.
5) Walk and run with your feet pointed straight ahead. This one is HUGE. Part of shin splints is an issue with repetitive impact and part is uneven muscle tightness causing bowing of your shins (PAIN). An older valet mentioned to me that this was the first thing his football coach made him work on in HS. Sometimes old knowledge is good, you know?
6) Take a small ibuprofen dose and/or ice shins at night. Sometimes things won't heal when they are all inflamed it seems.
7) Finally if you can, run on something softer. Asphalt is much softer than cement. Ask any jogger.
Hopefully these will help you get rid of the shin splints. I had them bad and had no option of not running. TORTURE I tell you! As always, rest is best. These will take time to work, 3 weeks or so if you are beating your legs up regularly and brutally
Curious to see how they work for someone else.