I did an internet search and I found one person on another forum who said kava gave them a runny nose. Kava may have some sort of decongestant or expectorant properties, but even if it does I'm not sure that would make your nose run.
I used to get this alot more when I was just getting off K@ . I used to assume it was just slightly agitating the opioid system in my brain. I'm not quite sure . Lol