What if the constituent of the brain changes, would you feel you or would it be like another person just go on being conscious. If you don’t know what makes consciousness, most likely you just “die” after the brain freeze. This ain’t like sleeping or coma where your system is kept running continuously
A somewhat different question, but interesting! I assume by clone you mean an exact physical copy, down to a molecular level.
In my view, there would now be two separate instances of "my" consciousness simultaneously. "I" would continue to see through the original one, but the copy would essentially feel the same as me, although increasingly diverging as our experiences would not be the same from that point.