Praise be to Allah.
If a fasting person eats or drinks during the day in Ramadan by mistake (because he forgot he was fasting), his fast is still valid and he does not have to make up that day or offer expiation. Please see the answer to question no. 50041.
The fact that you drank this water by mistake does not affect your fast, so you should have completed the fast of that day. As you broke the fast based on what your mother told you, and you made up that day, then you have done what is required of you, and you do not have to offer expiation, because expiation is only required of the one who breaks the fast during the day in Ramadan by having intercourse. Please see the answer to question no. 38074
And Allah knows best.