I agree. You can't compare the PH wire to the manometry probe. It's much smaller. That said, if you have a crazy gag reflux, you're not going to like when they place it. They can actually put you out to do that placement, but they'd probably have to make a special appointment.
Usually the GI doc's Nurse Practitioner does the placement. They'll numb your nose up, then thread the wire through your nose into your throat. That's when you'll feel it. They'll want you to help by giving a little swallow. If you have a deviated septum, guide them toward the larger nasal passage. Breathe, focus on something else in the room, and consciously relax.
The manometry takes a lot longer, as once they get it down they have you performing swallows. The PH wire is put in and that's all.
Like you, I always took the day off so I didn't have to be seen as much in public. My second graders wouldn't have liked seeing it! When you're coming and going from a medical facility, people expect to see things like wires coming out of someone's nose!
You will feel it when you swallow, but since it's much, much smaller than the manometry probe, it won't feel like that.
It's only for 24 hours! You'll be very happy to get it pulled the next day!
Good luck! You'll do fine.