Gills

My, you're looking green around the gills.

Incidentally, that the gills of fish are bright red is because there are many 'capillary vessels' collected there, the same as for lungs.

I ate until I couldn't eat any more. I was stuffed to the gills.

You look a little green around the gills.

Tom was looking green around the gills after eating something at Mary's party that didn't agree with him.

Fish have gills and fins.

Dolphins don't have gills.

Whales don't have gills.

Neither whales nor dolphins have gills.

The opah is equipped with specialized blood vessels that carry warm blood to its gills to rewarm the blood that cools as the fish breathes and absorbs oxygen from the water.