Definitely keep up with the Doc stuff. Even if there is nothing, if you are like me, it will help your anxiety to know all is okay. When Docs think it is medically warranted to check you out there is not reason to second guess it.
On the flip side, I got to say while I wouldn't describe it exactly like you are, I have had very similar feelings in my chest. Mine feels like it is a sharp pain/pulling between my ribs. But at times it is a burning in a specific area. I have had ECG, an Echo, and a stress test with all normal results. Mine also never reproduces when I push on the spot.
I hear you about this Health Anxiety stuff it is no fun. The more I accept that it is there and that I am okay, and can be okay in the future even if the symptoms don't all go away, the better I am (See some of Pan's posts). Try and concentrate on studying and those pesky midterms. Good Luck...