How do I find the power of a specific frequency at a specific sample of a discrete time varying signal?
I realize this doesn't answer the detail of what you're asking, but I believe it answers the question in the title:

See Rick Lyons's writeup here for using the Goertzel algorithm to get the signal level at a specific frequency.

You can then follow up the equations:



with:

$$
\hat{p}(n) = | y(n) |^2
$$

and use $\hat{p}(n)$ as your "instantaneous power" at frequency $\omega =2\pi m/N$ --- which is sort of like  Lyons's eq. 13.83:



(though he's evaluating this one at the "end" of his DFT length).