All you need is a P-100 or N-100 rated face mask (link below).This looks
like a surgical mask and is a HEPA filter. This is the best filtering of
air you can get. You could wear this on the plane and just explain that you
have allergies or whatever. Construction safety equipment stores should
have these. FYI - It is my understanding that most new large aircraft have
HEPA filters installed in their air systems. Also hospitals use these to
filter the air as well.

I use these masks when sawing pressure treated wood. Also I have stand
alone HEPA air cleaners which do wonders for my allergies.

If you were to wear something with canisters which looks like a gas mask,
it might alarm some of the other passengers. (The cartridges are for
chemicals, not particulates floating in the air.)

And those cheap 50 cent masks (not rated) at the hardware store are
useless.

P-100 face masks...
http://www.allergybegone.com/honfilmas.html