I currently have the stomach flu. I can not sleep due to this excessive amount of saliva every time I close my mouth. Any suggestions please help?

OTC Priloes or Preva. Use over the counter acid suppressive meds like Prilosec or Prevacid (lansoprazole) to reduce the acid production in your stomach, during your short illness, if still having symptoms follow up with your physician.
Use Antacids. Speaking more from personal experience than from medical perspective, you may want to swish with an antacid like maalox or pepto bismol (bismuth subsalicylate). The excess salivation is probably due to the regurgitated stomach acid in your mouth from vomiting. The antacids will counter that some and reduce the bitter taste as well. Good luck.