Is this an allergy or an intolerance?

Whenever I have milk products (milk, butter, cheese, etc.) I always get a stomach ache after a while followed by stomach flu-like symptoms. This has only started recently and I intend to see a doctor about it, but can't just yet. Keep in mind, I don't throw up when I eat these but I very much feel like I could.

Does this sound more like an allergy to dairy products or lactose intolerance?