If $$\left(4y - \frac{4}{y} = 13\right)$$, find the value of $$\left(y^{2} + \frac{1}{y^{2}}\right)$$.

A

$$12\frac{11}{16}$$

B

$$10\frac{9}{16}$$

C

$$12\frac{9}{16}$$

D

$$8\frac{9}{16}$$