How should I care for my skin after removing blackheads?

I get sebum around my nose.

Something that seems to disappear but then comes back to life

I'm concerned about it. What to do after sebum removal?

Do I need to manage this?

My daughter also has sebum around her nose, and dark spots.

It looks like sesame seeds, and I get white sebum.

Are the care treatments different after sebum removal?

Please tell me how to manage it.