It's not a case of not giving any hay, just shake it out lots. She still needs her regular fresh hay.
It is worth considering what else could be irritating her. One thing to think about is whether she sneezes most when fresh bedding is put in; in the cases of fleece/Vetbed users, maybe the detergent hasn't rinsed from the fabric effectively and is bothering the pig. For those using traditional bedding, perhaps the Megazorb/Carefresh/Aubiose etc. doesn't suit that pig.
The hay may be 'dusty', even those specifically labelled Dust Extracted are not usually that dust free. The only hay I have found thus far to be truly free of dust, is Dust Free Hay, no amount of shaking it out leaves plumes of dust in the air. Even Oxbow can be a little dusty. It's a worthwhile habit to get into to shake each handful out inside a big cardboard box, get as much off as possible before feeding to piggie.
If you can build up a picture of what is happening around Norah when she sneezes, it may help you and the vet determine if it is more likely to be allergy/sensitivity to something specific, or something else. Details I would list include:
Date
Time
Pollen count (if known)
How long since last full cage clean
How long since you put fresh hay in
If the windows have been open
If any air freshener/aerosols were used in that room or the neighbouring room in the hour before sneezing starting
If you did any dusting in the same room
Something may become apparent within a few entries. Keep with it for as long as you feel necessary e.g. until you have spotted and removed the irritant and the sneezing decreases.