How would the pole and zero frequency expression look like for this transfer function I derived?
If you look closely in the generic transfer function, the \$s\$ operator is single, everywhere, and there is a gain parameter. So try to isolate those from your t.f.:
$$\begin{align}
\dfrac{g_m-sC_{gd}}{s(C_{gs}+C_{gd})}=\dfrac{-C_{gd}\left(s-\dfrac{g_m}{C_{gd}}\right)}{(C_{gd}+C_{gs})\left(s-\dfrac{0}{C_{gd}+C_{gs}}\right)}=-\dfrac{C_{gd}}{C_{gd}+C_{gs}}\dfrac{s-\dfrac{g_m}{C_{gd}}}{s-0}
\end{align}$$
Which is a pure integrator -- that makes sense, since you have no resistive elements, only capacitors and a current source. Notice the denominator now shows the zero valued pole (as mentioned by Chu).