Rarely, dizziness may be due to a serious medical condition. These can include an acute stroke or a brain tumor, especially if accompanied by other concerning symptoms, such as dis-coordination, headache, or weakness. It is unlikely that the dizziness is related to your stomach condition. I the case that your 'digestive problems' were related to a stomach ulcer or other source of intestinal bleeding, chronic loss of blood could lead to anemia, which could cause fatigue and dizziness. If your bowel movements are occasionally dark black in color, this possibility is more likely.