"shoum" is "shu'm" (شؤم) in MSA, and it means "bad luck, misfortune". I don't know what bad luck has got to do with يا عيب الشوم (meaning, "how shameful!, how disgraceful!"), but maybe people thought that doing something bad is an evil omen.
Please note that يا عيب الشوم is the same as يا عيب الشوم عليك (= "shame on you!"). However, some people use يا عيب الشوم مِنّك to say something totally different. It's the same as "You shouldn't have" in English (Wiktionary: "Used to express gratitude at unnecessary generosity, especially when receiving a gift.") Just make sure that you say مِنّك