You have one consciousness ,not two or three.No scientists ,not even the greatest minds know exactly what consciousness is.
I think what confuses many people ,and what creates endless thoughts is that words are being used without actually really knowing what they are.You have one body and one soul (which is part of your consciousness).
What exactly do you mean by split conscousness ? Is part of you saying you should be happy and one part is saying you have DP/DR and you should think about it ?
Do some complex things and you will notice that you cant think about two things at the same time.When you feel like you are thinking about two thinks ,it is not because you can do it ,it is because your brain alternates between two thoughts.
And regarding thoughts ,you are not you thoughts ,remember that very instant moment when you wake up where you dont think about anything ? This is your pure consciousness ,and your thoughts are ideas inside your vessel ,dont give the negative ones any importance.