Is this p-hacking?

Hello, I’m in the process of writing up a masters thesis and I am compiling my data.

I am looking to test the effect of an injury on the L vs R side of the brain, as well as test the effect of a treatment. Due to these two variables, my supervisor and I deemed a two way anova most appropriate.

My data is paired, in the sense that I have measurements from the same exact mouse on the L vs R side (with the R side being uninjured). I think this is valuable information to retain, since there is variability mouse to mouse, so pairing it with its own contralateral brain value seems best. Because of this, we’ve talked about running paired T-tests for each individual pair. This worries me though, because I get these sense that this might be p-hacking. My intention isn’t to pull out significance where there isn’t any, I just want to best represent the true changes happening, which I feel requires pairing. Is there an ethical way to do this? My supervisor seems to think we can display both the 2 way anova and the T tests but this seems sketchy to me.

I’ve been taught shocking little about p hacking or statistics in general throughout my education, so I’m sorry if this sounds obvious to most. I appreciate any input.