Drowning, or water intoxication happens because your electrolytes go out of balance, particularly salt - they become diluted. A healthy adult can actually drink up to 15ltrs a day (because of what their kidneys can handle), so don't worry!
It is, like others have said, about spreading it out though. Drink when you're thirsty or sip a 2 litre bottle throughout the day to keep hydrated.
I sometimes drink a 2 litre bottle before 10am at work and that's on top of making my shake in a pint glass and it's done me no harm. I have about 5 ltres water a day, plus copious amounts of black coffee and then 3 shakes made into a pint. I wee a lot, but you kind of get used to it. I used to wee a lot more, but was going before I really needed it, so started forcing myself to hold it a bit longer.
This is gross, but I measured my urine, as I thought I was going to often, yet I was only releasing about 200ml each time and now can comfortably hold onto double that