Is the acne treatment effective even if blackheads and whiteheads are present?

I have blackheads around my nose and small, bumpy, millet-like bumps on the inside of my cheeks, so I am looking into acne treatment. I'm not sure if the cause of the two is the same or different.

When I use nose strips or sebum removers, my nose looks clean for a while but returns to its current state after a few days, and on my cheeks, even after exfoliating, it feels like small granules remain.

Can I still expect effective acne treatment in this case? I am also curious if blackheads and whiteheads are managed differently when receiving acne treatment.

I would also like to know if it is possible to differentiate between areas that require extraction and those that do not during the acne treatment process. Rather than treating it aggressively all at once, I would like to address it step-by-step within limits that do not irritate the skin.