Chris Smith answered this question...

Chris - The reason for that is because you have various reflexes that are designed to protect your airway: there's a nerve supply, the internal laryngeal nerve, which is sensitive to everything touching your epiglottis inwards and down into your airway.

You need to defend your airway very carefully because if anything goes in there it could threaten your ability to breathe. There's a very profound choking reflex and that triggers a cough. It also triggers various secretions to happen, the idea being that it will lubricate your mouth and anything that's stuck will get free.

At the same time, the same secretory-motor system also makes your eyes water a bit. It makes tears come to your eyes and also what you're doing when you're coughing and choking, you're blowing air up your tear duct. Normally the tears that you've got in your eyes drain down little punctum which is a little plug hole in your lower eyelid towards the middle. They go down towards the naso-lacrymal duct and drip into your nose. If you raise the pressure in your nose by coughing, sneezing, blowing your nose the pressure is reversed. It pushes the tears back up your tear duct and into your eye.

So there's two things going on: one - you increase the secretions, and two, you probably jettison some tears back into your eyes!