For humans, yes. Lesser creatures may be self-aware (the greater the brain the greater would be the capability for this). Creatures lower than humans, with simpler brains, would have a narrow range of free will. In most cases, lacking the capacity for abstract thought, they are probably at the stimulus-and-response level. We're a bit more complicated than that.
Self-awareness is just self-awareness. You can see it in a dog or cat that suddenly realizes that it is the center of attention and people are laughing at it.
Choice and will are will-o'-the-wisps. A dog meandering about the neighborhood sniffing the droppings and checking out the garbage cans is making choices all over the place--or could he do anything else? A man ducking out on his wife to visit the local dive is making a choice, or could he do anything else? You can argue that only the human has free will, but my cat is "good" and uses his litter box when it amuses him and the carpet when it doesn't. Maybe he can't help himself and maybe he has free will. Darned if I can tell from outside his head.