I think that the important thing here is that I can tell you what it isn't........it is't cardiac pain (it is not coming from your heart.)
You do mention any cough, so we can assume that it is unlikely to be coming from your lungs.
Being persistent and not related to food, I think that we can rule out a gastric problem (hiatus hernia), which only incriminates a musculo-skeletal problem ( have you done any lifting?)or a psychosomatic problem ( depression perhaps)
Well ther you go....something to think about.