Sounds like the intercostal area. Which may be a slight rupture/tear. Has happened (sooner or later) to many BB'ers.
You may not want to ice the area before training. Ice will only constrict the blood flow and you need a warm and active blood flow to the muscle worked. Actually might use a heating element, like a lotion, patch, gel, etc to keep the region warm. Heat brings more blood, which will also nourish the muscle area and help with healing.
An intercostal injury is hard to train around. If matters seem not getting better (or worse) than might suggest taking a couple weeks off on any direct/pressing chest training. And than come back to chest work better than ever.
Good Luck.