The texture or viscosity of the milk--say, 100% whole milk vs. 2% vs. skim--could trigger a gag reflex if you're not used to the thicker stuff or thick liquids in general, but the stomach pain could be related to a sensitivity of some sort.
Often, lactose intolerance causes gas, diarrhea, bloating, or nausea. It can vary in severity--in my case, I drink Lactaid milk and usually use a lactose enzyme supplement before eating things like cheese, yogurt, or ice cream. If I forget or skip it, I might be okay...but on occasion I might end up running to the bathroom or simply giving thanks that I'm not in public and my hubby is tolerant of my, um, toots! (He's lactose-intolerant too, but also has a ton of other dietary issues that can lead to migraines, so our refrigerator is stocked with vegan cheese and so on for him.) Luckily for me as a lacto-ovo vegetarian, it works out ok!
Our bodies change over time without advanced warning. It can suck, but at least some of it can be mitigated if you're lucky.
As for the immediate future? It will likely resolve itself soon; drink some water and stick by a bathroom.