I’ve met other people who experience this, as well, but I have no idea why it might happen.
When I eat salty foods, like potato chips, the skin of my nose gets REALLY itchy/tickly. Particularly the very tip of my nose.
Why? This doesn’t happen with smaller amounts of salt, and it doesn’t happen with any other foods. And as far as allergies are concerned, I’ve never experienced this itchy-nose sensation in any other circumstance in my life.
What the beans is up with that?
Perhaps you have an allergy to iodine? Does your nose itch when eating seafoods?
Hmmm… I don’t eat seafood. Lobsters are big sea earwigs, as far as I’m converned. 
Okay, let’s assume it’s only iodized salt. Is it possible for an allergy to iodine to cause no other symptoms but an itchy nose, which goes away within 5 minutes of not eating the salty thing anymore?
I’ve come across iodine before, never had any reaction to it. That being said, I never ATE it. But I’ve put it on wounds and such.