How can I break out of a while loop, from within a nested case statement?

In the case where the user entered "y", you can exit both while and case:

break [n]
       Exit from within a for, while, until, or select loop.  If  n  is
       specified, break n levels.  n must be ≥ 1.  If n is greater than
       the number of enclosing loops, all enclosing loops  are  exited.
       The  return  value is 0 unless n is not greater than or equal to
       1.

In your case, you want to do break 2.