Where does the saying come from that someone turns greenish when they're sickly? Like you see in cartoons where a characters face turns green just before the vomit. I've also seen it said that drug addicts look green when they are rotting away. Anyway, I've never personally seen anyone turn greenish when they are sick. Even the way I wrote it, the term seems a bit odd, like picturing someone who is spring green, not caucasian with a weird tint to their skin. I also thought of using grey as a color, but does that fit with a term like sickening? (Feel free to criticize my grammar/punctuation as well )
I've seen a couple of people who were so sick that they actually seemed a little green- not emerald green like in the cartoons, but more of a greenish tint to their complexion. I'm no medical expert, but I always assumed it was just some sort of optical illusion caused by the paleness of their skin. Anyway, when I write about it I usually phrase it as "a sickly shade of green." The way you wrote it still makes perfect sense to me though.
Green is associated with nauseousness; the pallor you get in the face and the color of vomit. It is also the color of bad fish as in "green around the gills".