I'm a general surgeon and severely sensitive fairly recently diagnosed celiac (18 months ago), manifested as chest pain from decreased blood flow to my heart, and severe heart failure requiring emergency heart angiogram (which was normal) and several months of head-scratching by cardiologists. Turns out I'm the 27th world reported case of gluten-induced cardiomyopathy (impairment of heart muscle by an autoimmune cross-reaction to heart muscle cells) and pericarditis (the "shrink wrap" sac around the heart being inflamed). Having said that, irritation of the heart muscle, the heart sac (pericardium), or even the lungs CAN cause the chest pain described by many people (especially the movement to the neck, shoulders, or right arm). IF YOU HAVE THESE SIGNS IT COULD ALSO BE HARDENING OF THE HEART (CORONARY ARTERIES) AND SHOULD BE EVALUATED IN AN ER!!! Don't die of a heart attack ... and not everything is caused by gluten.
With that disclaimer, our brains cannot tell the difference between our heart, pericardium, esophagus, stomach, gallbladder, liver, bile ducts (drainage tubes of gallbladder and liver), and the first part of the small intestine (duodenum). So pain from any of these sources can cause the grouping of symptoms that many people are describing. The comment about pain in between the shoulder blades is typical of *gallbladder* attacks -- belching, bloating, feeling pressure across the lower rib cage/chest/upper abdomen (either or both sides). Please consider talking to your doctor of the possibility of gallbladder disease, especially if the pains come after eating fatty foods (more stimulating to the gallbladder).
Ulcers, celiac disease gradually remitting, hidden gluten, acid reflux [which can occur without chest pain -- just burping], irritation of the stomach, esophagus, or duodenum, poor emptying of the stomach ("gastroparesis"), OR heart problems are ALL possible. If your GI prescribes an acid-blocking medicine like Protonix, Prilosec, Prevacid, AcipHex, etc., and you're not better in two weeks -- it's likely not acid.
I hope this helps, and I'm eager to learn things from this forum! Thank you.