The algebra was vile and I likely made a careless error but I got

\(\displaystyle \frac{d^2y}{dx^2}=\frac{0.5-6y^{0.5}+24y-32y^{1.5}}{(1-16y)^3}\)

You don't need y' in your answer because you already know its value from the first part of the question.