The fact that you do not mention pain anywhere else, is a fantastic sign:D
I get this an awful lot and at first, yep I panicked to, then calmed myself down because I did not have the classic signs of a heart attack and after doing a bit of research, I discovered that GERD suffers get this a lot and guess what? I am a GERD sufferer - well was until I have meds to calm it down!
I shall not say what happens because I know very well that your mind will come up with these pains which will just add to your distress.
Many say that they know when they are having an heart attack, and do you know what? You can actually do something to stop it getting worse!!! TAKE DEEP BREATHS AND DEEP COUGHS EVERY FEW SECONDS and this will save your life!
When my left side starts hurting - just as you describe, I automatically breath deeply.