Since this only seems to be happening at home, maybe it's some kind of environmental thing... an allergic reaction to something in your house? Go through and look at everything...anything new in the last few days before the gagging started? Maybe I'm wrong, but I don't think it's the Plavix, because I would think that if there was going to be a reaction like that to it, it would have happened within a few days of first taking it, not two weeks later.
Has anyone in the house started using a new perfume, deodorant, cleaners of any kind? Is there a new piece of furniture, rug, pillow, some new plants/flowers in the house?
Have you had the windows open more? If someone outside is using any kind of pesticide spray or anyone painted a fence or stained a deck? The fumes from all those things can be wafting into your house through the open windows.
I know I'm kind of just throwing all this out there, but I think it's really suspicious that it didn't happen when you went to the vet. Was Nelson doing any gagging in the car? Can you take him outside in the yard and see if he still does it out there? At least you can try to rule out environment things this way.
My angel Snowball used to do that gagging thing whenever she'd get a "kitty cold" (herpes virus), that seemed to always come up when we'd have the house open (Spring and Fall). Snowball was an indoor kitty, but we'd take her outside with her harness/leash when the weather was nice. But every Spring and Fall, she'd get runny eyes, the gagging thing and sneezing. We were never sure if the outside air had something she had allergies to which brought on the "cold", but if we kept her inside, windows closed up, and nebulized her, within about a week to 10 days, it would clear up.
I don't know if that's what's going on with Nelson, but it's one thing to check, especially with the vocal breathing too. That sure sounds like allergy stuff to me.
I hope the gagging stops.
Carol and Angel Snowball *5/10/91 to 1/1/10*
and the gang