It means that being called "shady" made him uneasy. "stirred my stomach up" --like feeling queasy or sick to your stomach. Sometimes when something unsettles us we literally get an unsettled feeling in our stomachs. "Just hearing about all their suffering stirred my stomach up/made me sick to my stomach" something like that.

I agree with CJ, but I just wanted to add that I have personally never heard the sentiment phrased "it stirred my stomach up." It would be much more understandable if you learned it as "made me sick to my stomach," as CJ said, or "it made me ill." I would also add that it is usually used figuratively, not literally. Although you might feel "dread in the pit of your stomach," (another phrase which means something very similar (except that it means you feel afraid that something bad may happen)) no one actually expects you to throw up (vomit).