Why aren't the pores on my nose clean even after double cleansing?

On days when I wear makeup, even though I remove it once with cleansing oil or cleansing water and wash my face again with a foam cleanser, it looks like the sebum remains around my nose.

So, thinking I might not have washed my face enough, I tried rubbing it a little longer, but that actually made the sides of my nose and cheeks red and tight, so now I am reducing the irritation. I've also heard that washing your face too hard to remove sebum isn't actually good, so I don't know what to do.

Is it difficult to completely remove sebum from the pores with just cleansing? I am also wondering if regularly exfoliating sebum or dead skin cells during skincare helps.

My nose is oily, but my cheeks tend to dry out easily. Is there a way to manage both areas at the same time?