[Capsaicin](https://en.wikipedia.org/wiki/Capsaicin) produced by the various spicy plants (peppers, etc.) causes the burning sensation, and also an inflammation (swelling, tenderness). You just have taste buds that react to it to sense as “spicy”. It’s an oil, so it doesn’t dissolve in water very well; milk works because it has fats in it that can dissolve the capsaicin and take it away from your mouth / tongue.
The reciprocal substance is [Menthol](https://en.wikipedia.org/wiki/Menthol), which produces a sensation of cool, and also numbs pain and soothes the tissue. Menthol is produced by the mint plants.
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