What does this poem convey? What do you think this is about?

Okay, what i get from this is that the speaker is in love with his sister (and, just a guess here, they're ancient Greeks, on account of all the mythical references), and he is going to kill her, then himself, to prevent her from being with any other man, and so they can have their unholy (re)union on the river to the underworld. Whether or not the sister returns the love is unknown.