Are you having a Braxton Hicks contraction at this time? My BH's radiate up into my chest too, and I feel like a big weight is being set on my chest. Feel your stomach when you're having these weird sensations, and if your stomach is hard then it's a BH.
Blessings to you and the baby to be. If you continue to have this feeling in your chest, have the doctor take a listen to your heart. As long as you are sure it isn't contractions... I am thinking you mean high upon your chest and not just below the sternum. I ended up with an irregular heartbeat most likely at the end of my pregnancy and no one noticed until I was a few hours postpartum. It corrected itself both times. They said it was related to the stress of delivery and not to worry. I am following up on the diagnosis now. Most people don't think about us young, healthy pregnant women having something going on that isn't totally obvious. Maybe check your pulse next time. And don't worry, just be aware. Enjoy that precious baby!! Time passes too quickly... :)