It's probably a mistake to think that there's a single, persistent and coherent "you" inside your brain in the first place, even though it feels that way.
From cognitive science, the picture is really more like a loose and varying affiliation of various "consciousness applets", hosted in both hemispheres.
So the result of your thought experiment would likely be two impaired versions of your original consciousness, each lacking certain facilities but perhaps both enjoying a sense of continuity with the original "you". We know, for instance, that people can have improbably large chunks of cortex removed under local anaesthesia and retain a sense of continuous "self" throughout the process.

Grant Hutchison