Should I filter before calculating power, if I'm looking for relative changes in power?
If the output from the SDR matches the band you're interested in, I see no point in filtering.

You want to filter when you have a scenario similar to this: you want to track the power in a band of $B$ Hz around a frequency $f_c$, but the SDR's output covers a band that is larger than $B$. In this case you want to filter, since otherwise a signal outside the band of interest could affect your calculations.