Mark, the flaw which first springs to mind is that you seem to presuppose that if God is omnipresent, then he must also be corporeal and temporal (he exists in space and time).
But God is thought by those who believe in him to be eternal, meaning his existence is atemporal, outside of time. He is also thought to be incorporeal; his being is sometimes described as 'pure being'.
So God's omnipresence cannot be of a physical or temporal kind. But my presence is both physical and temporal. This means the question whether I am God, or part of God, cannot arise. God and I have utterly different modes of being.
I suppose a theologian might say that God is indeed omnipresent, but on another dimension (as it were), one which we cannot perceive or even imagine. Or, since God is omniscient and omnipotent, it is as though
he were present everywhere; he knows everything that happens, and could intervene if he wished.
Like most of God's alleged attributes, the concept of his omnipresence is difficult, confusing, and probably ultimately absurd.