Pig sick is when you feel very sick. Not to the point where you need to go to the hospital, but sick enough that you can complain to all your family and friends and instead of laughing at you, they actually sympathize.
Person 1: "Just how sick are you?"
Person 2: "My head hurts, I have a runny nose, and a sore throat."
Person 1: Woah, you are definitely pig sick."