It is very normal to have your nose run while doing cardio. I, also, keep a box of kleenex next to my TV/DVD/VCR player.
I have had quite a few sinus infections over the years and I remember telling my nose/throat/ear specialist how when I would workout my sinus's would unclog and clear up my congestion. He said aerobics always clears one out - he also suggested I just do cardio all day on se days that I was totally clogged up on. HA-HA!
Everytime I spar during my martial arts classes, I always get a runny nose, too. It can be very annoying!
Cheryl