Kitten has been sneezing for 3-4 weeks now

I had a dog as a kid that went thru a sneezing fit like this once. It
went on for weeks. Near the end, he would slam his head violently into
the ground as he would sneeze. I soon found out why.. Finally, upon
one supreme sneeze, a small green shape started to emerge from one of
his nostrals. It was a long single blade of saw grass. It had
backwards slanting fibres on it that ran it's entire 8 inch length,
allowing it to move forward but not back. It just took time to work
itself thru his nasal system to a logical outlet.
Do you let your cat outside?

I wonder how that blade got into his nose. Any ideas?