You are correct. The veins in the sinuses swell causing the feeling of a stuffy nose. Menthol and those vicks sinus smelly sticks cause the veins to contract, making room for more airflow to move through. I recently remembered the vicks sticks my grandmother used when I was a kid and looked it up to see how they worked since you don't actually inhale any fluid/medication.

If you get too strong of a dose, sure you might close the sinus spinxter (?) muscle on instinct.

But that "cool" effect of guns, toothpastes etc is just triggering the receptors with false signals.