Okay. I was wondering. If a person swollows water and it goes down their windpipe does the water stay in it?

Not usually. Cough usually clears water less toxic than some chemicals and solids which can choke and suffocate..
Lymphatics. Your body has a remarkable plumbing system know as the lymphatic system. This system is designed to help remove fluid (water) and infection from the lungs by pumping the fluid out of the chest to other "safer" locations in the body. The system can become overwhelmed however when someone takes in large amounts of water (ie drowning).