I've had the same kind of soreness myself, and my doctor diagnosed it as costochondritis. It's inflammation of a rib or the cartilage connecting a rib. It can take a long time to heal, but you should go to a doctor about it because he or she can prescribe a stronger anti-inflammatory than you can get over-the-counter. When you have this kind of inflammation it tends to get worse unless you treat it.
Another thing it can be is mastalgia (breast pain), which is really common in younger women who still menstruate. The more common type (cyclical) coincides with your menstral cycle, like a few days before your period when you're retaining water. That could be it if you've noticed it being worse on certain days of the month. If anti-inflammatories don't help, hormone manipulation could do it. Either way you should see a doctor to rule out a more serious cause.
As for the chest pain, it could be related...or not. I would always err on the side of caution when it comes to chest pain. It could just be a muscle strain from exercise or from lifting improperly. But wouldn't it be reassuring if you knew that for sure?
Hope this helps some.