This can happen if you are not drinking enough water. When you get up and then drink something all the toxins that weren't cleared the day before flood your system and you just feel gross and nauseated. Consider carefully stepping up your water intake. And if you don't have reflux consider not taking the acid reducers, they hamper digestion.
No. Don't. It's a really important part of your digestive system. Unless you have something irrevocably wrong with the gall bladder, I'd leave it right where it is.