Could i rid of a sinus headache by drinking water?

Maybe: If you are dehydrated, this will help. If your urine is dark yellow, you may be dehydrated. Consider a water with a pH of 8.8.

Unlikely.: You can try. It might help hydrate your mucus a little more and if it indeed does, it will clear better from the sinus. The inflammation of the sinuses will not improve and might still cause the obstruction that causes the mucus to impose pressure on the sinuses. Seeing the doctor after having tried anthihistaminics, saline flush, is always a good idea.