I am also a heartburn sufferer having Gastric reflux disease, for me personally the burning sensation is not where you describe at all, mine is in the middle, it sounds more like a gallbladder thing to me,(i cannot remember which side it is for sure though) but I think it is the right if my memory does not fail me ,appendix is way lower down I think, but you should really just go to a Doctor and find out for sure, if you think it is heartburn try some over the counter antacids, if it does not improve , then it is not that or more like GRD which does not respond to antacids,hope you feel better soon, pain is not a nice experience.