I don't have a Vive but rather a Rift but have never heard of anything like this. Given you say it gets better when you take it off that does make it seem it's the Vive. Do you have any other allergies? What is the face guard made of, fabric, leather or plastic? Have you tried placing something between the face guard and your skin, maybe even some tissue paper as a test?
Very odd - very curious what you figure out. Do you ever wear ski or scuba goggles? Do you have anything like that to test with? I've worn my Rift for 12+ hours straight a few times and while my face gets a bit sweaty and it'll leave a mark after that much time I've never had a reaction like that. Bummer for sure.
The noseguard thing is removalable, it just pops in and out.
It could be pressing on a nerve or blood vessel if the sensation returns to normal after taking it off.
Before getting the VR covers for the Vive, I cut out a bunch of single use covers from "Press'N Seal" that I would wrap around the foam thing. When we'd have friends over, other people's sweat soaking into the foam was a bit gross.
Owning both the Rift and the Vive though, I find the Vive more comfortable now it has been adjusted!