Mustard and horseradish are both in the family Brassicaceae (used to be Cruciferae) and their most prominent flavour components are chemicals called isothiocyanates (nice tongue-twister, I always thought!) In fact, the two most prominent of the isothiocyanates are allyl isothiocyanate and 4-hydroxybenzyl isothiocyanate. The former is most plentiful in black mustard and in horseradish, as I remember, and the latter in white mustard.  Allyl isothiocyanate is sharper and more volatile, so you are likely to breathe its vapours up your nose, where it burns the sensitive mucous membrane, hence Jonathan Swift's cliche in his "Polite conversation": "...your Mustard is very uncivil ... it takes me by the Nose".  4-hydroxybenzyl isothiocyanate is not so fiercely stinging, but it settles down on the skin and burns for longer.

Some of the pure isothiocyanates, especially allyl isothiocyanate, among those that we normally experience, are shockingly vicious; a mere whiff of allyl in particular sneaks up your nose and smells rather nice for perhaps one second, then settles down and scorches you with a feeling that your mucous membrane is on fire. They are not for playing with; some can cause dangerous blistering. STEER CLEAR of dangerous mutts that might want to play with the stuff. That way blindness lies. But if you boil a seed before crushing it for mustard, or quickly crunch it dry and swallow it, it has little taste; conversely, if you mill dry mustard seeds and soak them in warm water for a while, you get mustard too vicious for most people to use.

The thing is that the isothiocyanates would kill the plant tissue, so the cell does not stores it as the final product. Instead it is accumulated in a fairly harmless precursor form, delicately separated from an enzyme that will convert it if the cell is damaged so that the two come together, warm and wet. That way the dying cell can get some revenge on the creature eating it, possibly harming it or teaching it to eat other things instead.

So: Choose your mustard more carefully. French and American recipes are less vicious than English mustard. White mustard is less sharp than black, and you might find that by holding your nose or breathing so that air from your mouth does not exit from your nose, you avoid the sting.  You would have to compromise though; you need traces of the aroma up your nose, or you will hardly get the benefit of the mustard flavour.

Life's frustrations can be very complicated... Ask anyone in love!

Bon appetit!  

Jon