I had what's called, "machine gun sneezing" from the damage to my Vagus nerve.
And, yes, I also had post nasal drip a lot with the band. Some people seem to get the sniffles as a "stop" sign... and others just get the sniffles, no matter what.
I took Allegra D and had to avoid doing crunches or bending "wrong." If I bent a certain way, I'd be sure to bring on a sneezing fit that would last for hours. I passed out from sneezing once and chipped a tooth! It was crazy! Saw so many docs and they were all clueless... didn't know about banding, the Vagus nerve, nuttin'! Finally, I found one who was educated and was able to help me.
What concerns me, though, is that this could be a sign that your diaphragm and the nerves are being irritated. Do you experience any left shoulder pain? Or is it just the post nasal drip? Have you talked with your surgeon about it? Do you find that any medication helps?