I get an upset stomach only when I drink ...
I drink strong unFlavored Coffee without problem.I can use flavored cream at home – again, no problem. The problem arises when I drink flavored coffee from a cafe. I’ve tried opting out of whipped cream (at places like Starbucks), but that didn’t help. The flavoring seems to be the only logical culprit, but I’ve never seen anyone else comment on this as a problem.
Do you mean that you are drinking things like lattes at coffee shops?
If you are, your stomach is probably not used to that much sugar and milk at the same time. How fast you drink them also plays a factor in this.

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Denis Leary talks about trying to get a cup of coffee