Jessica - one thing about the heart is that there are no pain sensors there, so any "pain" is felt elsewhere.

I have bad upper back pain, and that hurts my chest quite considerably. But by all means, go to the hospital, emergency ward or to your hospital birthing centre. Once you're there, its harder to leave until they've worked out what's wrong. Are you able to leave the little one with a neighbour? Or call someone else to meet you there?