I can't seem to keep water out of my nose.

I've just started practicing my freestyle kick with a snorkel and can't keep water from going in my nose. I feel I made good progress with my kicking technique tonight, but I still never even made it from one end of the pool to the other without raising my head because I was about to choke. The build-up of water was always very gradual; I felt my nostrils filling up but pushed on until I felt water go down my throat and had no choice but to stop and lift my head. Should I get a nose plug, or should I keep practicing this way to see if I can overcome the problem? How common is this situation? Are there some people who are simply unable, for anatomical reasons, to keep the water out of their noses? Thanks.