Shin soreness and shin splints are often caused by hi-impact activity, such as running, etc.
Personally, I'd recommend that you avoid hi-impact activity until such time as you have no more pain or soreness.
As far as treatment is concerned, ice the area at least once each day for around 20 minutes, but don't apply ice directly onto your leg(s) but rather use an ice bag or wrap ice cubes in a cloth bag or flannel, etc. You should also stretch the muscle on the front of the shin regularly. Feel the pull, but don't cause intense pain in the muscle, and don't 'bounce' stretch in any way.
Does anyone know what I can do to avoid pain in front of tibias (shin splints) when practicing savate (or as warm up)? I tend to get this as I usually do high-impact sports 1-3 times a week combined with being stuck on a chair the rest of the week, or after being away for a few weeks without doing much sport..
For running, shock absorbing shoes seem to help but it doesn't seem to do the trick with savate.
It's not so bad after a few minutes of practice as I suppose the muscles warm up, but the next days are usually a bit oumf!
