No, I am not my body, or even my mind. My self-identity consists of thoughts and ideas which I recognize as belonging to me, and are dictated by my will. These thoughts and ideas were not of "me" originally, but rather, they were acquired from the outside world.
The "I" that I recognize is vastly different from the variety of unconscious processes and instincts which my mind contains, and which my body experiences. I am not directly responsible for, nor am I in control of, my heartbeat, my ability to experience physical pain/pleasure, emotions, etc. My body exists, and "I" exist within it, but I would not acknowledge that the two are one and the same.