It is proposed that it is possible that a person may develop two separate conscious entities within their one brain after undergoing a corpus callosotomy.
So unless you've had your brain cut in half to treat your epilepsy then you're probably alright
No conclusive evidence of the proposed phenomenon has been discovered.
The one thing I can think of that approaches support for the idea is "Joe, the split-brain patient"'s case. You can show him stuff on the right side of his visual field, and he'll tell you what it is. Show him something on the left side of his vision, and he can draw it and react to it, but can't name it. The speech center of his brain is disconnected from the right hemisphere due to that procedure.
This video by CGP Grey goes into it a bit more, but split brain patients have even had their two halves disagree. For example the conscious hand picking out something to wear then the other hand batting it away and picking something else. It's quite fascinating to read about.
It's definitely a fascinating subject! I guess the big question is whether we all have two consciousnesses already or that situation only develops after the split. It seems to me that healthy brains have both sides working so well together that they're essentially one unit, and they only start behaving separately once their forced to.
In those experiments, the speaking portion of Joe has no clue what the other side is experiencing. Like they show it to him on the wrong side and say "can you see this?" "No". Then they ask him to draw it, and to his amazement he does. It's not just being unable to vocalize certain thoughts - they're not even there to vocalize at all to that part of the brain. But the other half is happily chugging away with that info
ooo theres a video where they experiment on a guy that had this procedure, like trying to show different objects to different halves of his brain. its freaky and interesting, wish i could find it.