The cartilage around your chest bone can cause pain in the middle of your chest. That's the cartilage that connects the chest bone to the ribs. You might want to ask your Dr about costochondritis causing any chest pain. It's very common. It's basically spasms with the cartilage that joins the chest bone with the rib cage. Some people mistake it for heart problems. It's harmless. It comes and goes. Exercise your chest and stretching movements in your chest can help with it sometimes.
Also, you may ask about getting an MRI to see if any back discs are pushing against a nerve. X-rays will not show that kind of thing. Only an MRI.
I had this exact thing happen to me with all three of my children. Oddly enough it turned out to be heartburn. After i brought up the possibilty that it could be something this simple i was diagnosed with acid reflux. I know during pregnancy Tums are safe to take however i do not know if any others are. i would check with a pharmacist or call your doctor to find out what over the counter heartburn meds you can take. i hope this helps and i hope you feel better soon. good luck with the new baby :)