设函数 $f\left(x\right)=\left\{\begin{array}{l}{x}^2+1,x\le 1\\ \frac{2}{x},x>1\end{array}\right.$,则 $f\left(f\right(3\left)\right)=$（）.

A．

$\frac{1}{5}$

B．

C．

$\frac{2}{3}$

D．

$\frac{13}{9}$