I have learned to add real cream, real butter, real cheese, and cream cheese to any hot chili dishes. Oil  and dairy help to calm the burning sensation. Water makes the experience worse.

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I think you're right about cream/dairy.  Also a little sugar helps. So the best antidote must be ice cream.
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Water makes the burn increase, true. 
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In the end, it takes TIME. Nibbling on some ice cream can soothe the burn, but the moment you stop having ice cream it comes back with a vengeance. And the ice cream seems to prolong the time the spiciness burn keeps trying to return. Eventually you have to ease off on the ice cream and just let the burn have its way. It will swell hotter on your tongue for a moment, but then settles down.
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After a year or two of practice you don't have any more discomfort, and the spiciness burn is very much reduced.
There comes the day when spiciness turns into an appetizer, whereas it used to be a turn-off. That comes with maturity. 

Don't miss an opportunity for Chile Rellenos.  :ready-to-eat:

Hands down my favorite Mexican dish.

A good Mexican restaurant will have soup. I love their chicken tortilla soup. However, it's made differently everywhere I have gone. Sometimes its chicken soup with tortilla noodles. That and a side of rice and salad should be fine.

Sopa de pollo?