Particle System - Timing it to an Animation Clip

I have a character whose nose catches on fire when he sneezes, and I used Unity's Particle System to create that fire. However, there are several other animation clips attached to the character, and I only want the fire to play during the animation clip I labelled "Sneeze".

Is there an easy way to do this? I have a deadline to meet and am in urgent need of a solution. If the solution requires coding, my knowledge of C# and Javascript coding is at the level of an absolute beginner, but I am very willing to learn.

Many, many thanks in advance!