Drinking water is a good thing, but drinking copious amounts of it can be extremely dangerous. It can cause hyponatremia, which is a life-threatening condition; 16 glasses would probably be enough to trigger this in some people if they are hydrated in the first place.
Fiber supplements can be tricky in the beginning because they do increase discomfort until the body adjusts to them. So starting them off very slowly is usually the best way to go about it.