Here are some of the things Jesus says about Himself in the Gospel according to St. John:
I am the bread of life. I am the living bread that came down from heaven. I am the light of the world. I am one who testifies for myself. I am the one I claim to be. Before Abraham was born, I am. I am the gate for the sheep. I am the good shepherd. I am the resurrection and the life. I am the way and the truth and the life. I am the true vine. I am. I am a king.
The two hyperlinked statements got particularly strong reactions. The first caused people to pick up stones to throw at Jesus, the second to turn away and fall to the ground.
I wonder if we can learn anything by taking note of the things we say about ourselves, the predicates that follow our saying, "I am...." I haven't tested it, but my hypothesis is that a lot of us would catch ourselves saying things that don't fit well with, "I am I AM's child and heir."
A more speculative hypothesis is that a lot of the things we predicate of ourselves that could fit with being I AM's child and heir we don't actually mean in that way. I might say something like, "I am the driver of this car," and mean it in a categorical and absolute sense, entirely free of both my creaturehood -- the fact that, whatever I am, I am by an existence loaned from God -- and my sonship -- the fact that I am supposed to be in all things like my heavenly Father. If I watch what I say about myself, though, I might become both more humble and more faithful.
Speaking of which, here (by some translations) is the final predicate of Jesus in St. John's Gospel: