You're describing conflicting imperatives coming from different brain centers, each of which are made of neurons functioning outside of consciousness until they deliver a message to consciousness. Suppose that you've got surgery tomorrow, and can't drink after midnight. You become a little dry, your hypothalamus, which measures plasma osmolality, reports the urge to drink to consciousness. Prefrontal neocortex sends a conflicting message to not drink, and you don't.
Many posters on this thread are calling that second neural center self even though it acts outside of consciousness generating what becomes conscious ideas. Two wills from two brain centers are in a tug of war and one prevails. Do we say that one is us but not the other. This is an arbitrary choice in my mind. The hypothalamus apparently doesn't enjoy free will, and we don't choose what it tells us to want, just whether to obey it or not.
So why is one piece of neural circuitry informing the self of its output considered part of the self and not the other? We can just as easily frame this as two pieces of brain opposing one another with one being stronger, and the self the passive observer of this. If we do, where's free will now? Even if we identify with the neocortex, what's free about the way it works before sending its output to consciousness?