If it was Mango skin, I would expect the stomach to digest it. It might sit in your stomach longer, perhaps quite a bit longer, than food that had been chewed up, but the enzymes in the stomach and the upper part of the small intestine should digest it. Amylase, which digests starches (carbs) is emitted in the upper small intestine. Doesn't mean that you might not have a stomach ache for a few hours, but I don't think it will pass through your system intact.
If it feels like it is still in your stomach, take some digestive enzymes if you can get some (should sell at the health food store) or take some fresh papaya seed (which are high in enzymes) or even some fresh pineapple (contains bromelein enzyme) which will help digestion of the mango skin.
Also, the vagus nerve runs down to the stomach, and it could reflect pain up to the upper chest.