My impression of Anna was pretty much the angel idea you just mentioned, although more along the lines of a close friend or relative acting as the angel. But yeah, your way works very well, the inner self being the subject of the song. Both ways of representing 'anna' give a similar meaning to the song.

Just remember this, when (if) you become famous and release the song, people will be asking "who is Anna?" simply because they wont understand it until you tell them, and even then some people still wont understand it.

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This is my life! And there is nothing you can do about it!
To think that life is enough, is to be killed by your own existence.