Does celiac disease make it more likely that I'm going to get stomach cancer?

No. Celiac disease, especially if one has symptoms or small intestine inflammation/damage, does increase one's risk of small intestine cancer (adenocarcinoma, lymphoma). The increased risk may go to normal if one stays on a completely gluten free diet and stops having intestinal symptoms for many years. Celiac disease is not a risk factor for stomach cancer, according to the american cancer society.
Not stomach cancer . Individuals with celiac disease are more likely to have diabetes, thyroid problems, and other autoimmune problems in the GI tract like the liver. Rather than stomach cancer, the usual cancer that is found is non-hodgkin's lymphoma a tumor in the lymph nodes.