Fasting on Tisha B'Av while Breastfeeding

I am, thank G-d, fully breastfeeding my four-and-a-half-month-old son without any formula. Before each feeding, I need to drink two cups of water, and generally, I need to drink a lot. Therefore, I am concerned about the fast of Tisha B'Av. Is it possible not to eat but to drink?

Shalom!
Generally speaking, a nursing mother needs to fast. She should prepare properly for the fast by drinking a lot in the days before the fast and resting during the fast itself.
However, if indeed the fast would result in a lack of food for the baby, you should drink and not fast.
You can start the fast and see if indeed the baby lacks food. In case it does, immediately drink a large amount.
On Tisha B'Av, there is no significance in abstaining from food, but not from drink [unlike on Yom Kippur], and anyone who needs to drink can also eat.

Shulchan Aruch, section Orach Chaim, chapter 554, paragraph 5.