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Florence + the Machine – Swimming Lyrics 12 years ago
I think "the song" that she is talking about represents a relationship she has with a guy.

Sinking = falling in love
swimming = being hopelessly in love although in the song it alludes to something being wrong with the relationship
and if you look at the other elements, like an exploding life jacket, and jumping back in the water after seeing him, show that something is wrong

Just some thoughts

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