What am I? is a question that comes up as a result of introspection. It need to be answered, much like what is god? The answer is personal, no right or wrong, but possible a correct on not quite correct answer.
I is singular. It cannot be divided. It is the essence of me. Tolle struggled with this in his "I cannot live with myself"; Dante struggled with reality in his "I think therefore I am"; Epictetus resolved it to his mind, that which he had control over. In this way his body became unimportant to him, desirable but not within his absolute control. Kiss your own mortal ass goodbye, and go with god's plan, the non-plan, fate, fortune, destiny, what happens happens. Make it the best we can, live with virtue and nature, but without concern for self.
It seems that, in the modern human thought, the body us included. Yet this leads to problems in the psyche. So the body is out, as is the physical brain, but the mind and consciousness are still in contention. But what is the mind; not the physical structure, not the chemical reactions, not the synapses firing, not memory's, but more intangible than that, the energy of thoughts, not just memory. Memory is diluted with time, and dilutes with more time. I is timeless, it is instantaneous energy, a biological force of some kind, with its own rules of conduct, rules of being. Being a biological force, and with god defined as the sum of all forces, it is a bit of god. Energy is force acting over time.
Just as the body has it's rules, the consciousness underlies language, it is awareness, but not a physical thing, but sit on top the physical cell structure. Is this the intent of the buddhist concept of no-self, the non-existence of self, that there is no physical self, just a concept, a soul, an energy, a no-self? It does what it does. Acceptance is required. Just as the body obeys a unknown set of rules for us to discover, the self does the same.
Be well, breath, smile, and enjoy what life offers. Daoish.