Missy has a cold and has a lot of snot going on. The last couple of mornings I've had to bath her because she has spread it all over her face, eyebrows and hair

Her skin is very red and spotty where the snot was smeared (over cheeks & forehead but around her eye is the worst She does get a bit of eczema occasionally which I thought it was but now I'm not sure.

Is it possible the snot is causing this?