What you have described with your water analogy is Hinduism, and not Buddhism.
Buddhism does not teach that there is no self, or that there is non-self, but rather, that all phenomena is not-self (sabbe dhammā anattā).
A very apt analogy for this can be found in the Vina Sutta:
"Suppose there were a king or king's minister who had never heard the
sound of a lute before. He might hear the sound of a lute and say,
'What, my good men, is that sound — so delightful, so tantalizing, so
intoxicating, so ravishing, so enthralling?' They would say, 'That,
sire, is called a lute, whose sound is so delightful, so tantalizing,
so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go
& fetch me that lute.' They would fetch the lute and say, 'Here, sire,
is the lute whose sound is so delightful, so tantalizing, so
intoxicating, so ravishing, so enthralling.' He would say, 'Enough of
your lute. Fetch me just the sound.' Then they would say, 'This lute,
sire, is made of numerous components, a great many components. It's
through the activity of numerous components that it sounds: that is,
in dependence on the body, the skin, the neck, the frame, the strings,
the bridge, and the appropriate human effort. Thus it is that this
lute — made of numerous components, a great many components — sounds
through the activity of numerous components.'
"Then the king would split the lute into ten pieces, a hundred pieces.
Having split the lute into ten pieces, a hundred pieces, he would
shave it to splinters. Having shaved it to splinters, he would burn it
in a fire. Having burned it in a fire, he would reduce it to ashes.
Having reduced it to ashes, he would winnow it before a high wind or
let it be washed away by a swift-flowing stream. He would then say, 'A
sorry thing, this lute — whatever a lute may be — by which people have
been so thoroughly tricked & deceived.'
"In the same way, a monk investigates form, however far form may go.
He investigates feeling... perception... fabrications...
consciousness, however far consciousness may go. As he is
investigating form... feeling... perception... fabrications...
consciousness, however far consciousness may go, any thoughts of 'me'
or 'mine' or 'I am' do not occur to him."
The lute (vina) is a stringed musical instrument similar to a cello, that you can play by plucking. From it comes music. The different parts of the lute are like the five aggregates (form, feeling, perception, mental formations and consciousness). Music is like the self (which is basically a mental idea). One might think that the music is located somewhere in the lute or pervades the lute.
Using a musical instrument you can play nice music. But if you break it down to its constituent parts, you cannot find music. Music cannot be isolated from the musical instrument. Similarly, the self, is a thought in the mind that arises from the inter-working of the five aggregates. You cannot isolate the self from the five aggregates.
Perhaps, you can look at it in this way: The musical instrument is the sentient being. The music coming out of the musical instrument is the self. The musical instrument is composed of various parts which are analogous to the five aggregates. When these parts work together, they make music. The way they work together is dependent origination.
And that is a very nice and simple way to think about not-self (anatta).
