M.F.
I've had similar pains. It could be any one of a few different things. Could be acid reflux (pain from this can often be mis-referenced). Could also be that the ligaments, etc. in that area are strained or sprained. Hormones related to pregnancy cause changes in the ligaments all over your body. It's the reason some women have bigger feet or a bigger bra size (not cup size, but the measurement around). Everything that is holding your bones together just stretches out. Sometimes it doesn't go back to the way it was before the baby. Meanwhile, all of the muscles, etc. around those areas have to adjust to new positions...and it can be uncomfortable. I had a ligament problem in the chest/rib area and was told not to lift anything for a while, take some naproxen and it would go away. It did.
Also, because I worked for the American Heart Association for 5 years, I feel obligated to say that you should check with your doctor any time you experience chest pain. Women especially can have uncommon symptoms of the artery blockages that can lead to a heart attack.
It takes your body 2 years to recover from the effects of pregnancy, and every woman is different, so you never know what could be going on.