Drinking too much water can lead to water intoxication, but
For those who have healthy kidneys, it is rather difficult to drink too much water
(according to Wikipedia). Another article has information about the exact amount:
Healthy kidneys are able to excrete approximately 800 millilitres to 1 litre of fluid water (0.84 - 1.04 quarts) per hour. However, stress (from prolonged physical exertion), as well as disease states, can greatly reduce this amount.
Water intoxication may lead to
headache, personality changes, changes in behavior, confusion, irritability, and drowsiness.
and in the end, it even
is a potentially fatal disturbance in brain functions
Every substance is potential poisonous, it just depends on the amount. It's not likely you will get water intoxication from combating a toothache.
Water probably helped for you because it cools your teeth; an alternative could be using an ice pack. Even though you're not likely to suffer from water intoxication, it might save you a few trips to the restroom.