Sometimes seeing the "operculum" just inside the nare of a cockatiel can be confused with a blockage of some sort. You provided a great photo that clearly shows the operculum on your bird. Any of my smaller birds will sneeze and scratch their faces when they're on my shoulder and my hair tickles their faces which may explain why your tiel sneezed several times after being near your hair. Read this information and it may help you understand the inside of your tiels nostrils, how their own dust can affect them as well. If you still think there is a blockage you may consider misting your bird, having a vet check and if a vet visit isn't feasable because of current world conditions you may be able to send photos to a vet for confirmation of a possible blockage... be sure to add extra photos with good lighting including the one posted above.
1. My pet cockatiel sneezes more than my other birds; should I be concerned?
Pet cockatiel feathers make an excessive amount of powder, produced by the powder down feathers. This powder can make its way into the nares and upper respiratory tract of pet birds, including the dusty pet cockatiels that produce them. This can result in a bird sneezing to expel the excess dust, powder and dander.
As long as the sneezing is not continuous, and the sneeze is dry (it produces no moisture or mucus), it is normal. If you notice that the sneezing increases in frequency or intensity or if begins to produce mucus, then it will be time to have your pet cockatiel evaluated by your avian vet.
Consider running a good quality air filter with HEPA filtration in the bird room to clean the air of dust, debris, pollen, spores and powder down.
8. There is stuff in my pet bird’s nares. Do I need to clean it out?
When in doubt, have your avian veterinarian examine your pet cockatiel. He or she can tell you if there is a problem.
You can do the following at home to help: take your pet bird into a steamy bathroom while you or a family member showers, so that the bird’s respiratory system is kept moist. Try misting your bird with warm water several times per day.
All cockatiels have an operculum inside the nares, which is a keratinized flap. Sometimes the powder down may accumulate inside the nares, over the operculum. That’s why increased humidity will help dislodge and remove any debris.
Never stick a sharp object into pet bird nares to dislodge debris. If that is necessary, your avian veterinarian should do it.
The two articles are copied and pasted from this link:
Pet Central looks at the top 10 pet cockatiel vet questions & answers, from illnesses and hygiene to laying eggs.
petcentral.chewy.com