I eat low carb and drink and I never have a problem with it.

But keep in mind, There isn't a NO carb diet. Even on Atkins induction phase you eat 20. However some people need ore and it says in the book that if you are feeling sick, you need to add a few more carbs. Atkins is the strictest one too.

It sounds like you drank on an empty stomach and got sick from it. Always drink after a meal, alcohol as a tendency to spike in unpredictable ways on an empty stomach. Plus without anything int here alcohol could irritate your stomach.

I bet if you keep your carbs more around 30 and spread them out a bit, and drink after a meal, you would be just fine.