Fortunately, that hasn’t happened to me yet. But I do have a funny story:
The first time I ordered for myself at an Indian restaurant I had no idea what to get. I was with an Indian friend of mine, so I asked him for suggestions, and we talked about what I might like. I settled on a chicken tikki masala, I think, at “medium” hot. He ordered the same thing for himself at “hot”.
My dish was excellent, hotter than blazes and teetering on the edge of my capability. I had to eat pretty slowly in order to avoid sweating, tearing up and just plain giving up. It was delicious. My friend… couldn’t finish his. It was too hot for him.
But my suggestion for stopping the burn, since milk and dairy products just don’t do it for me, is acids. Lemon juice and vinegar work well to cut the oils for me; I suppose any (palatable) acid would work just as well.