Is it possible to manage nose sebum, pores, and small blemishes at the same time?

I would like to inquire if it is possible to manage not only the sebum and enlarged pores around my nose but also the recurring small blemishes. I do not have severe acne all over my face, but bumpy areas appear next to my nose and on the butterfly zone, and sometimes they turn into small red blemishes.

Since my skin isn't smooth, those areas stand out even more when I apply makeup, and by the afternoon, sebum even surfaces, making my whole face look messy.

Squeezing out sebum with my hands or aggressively exfoliating makes my skin look better for a while, but the problem recurs after a few days, and my skin frequently turns red. I would like to get a proper consultation now. I am wondering if there is a way to manage clogged pores and minor blemishes at the same time in cases like this.

I would also like to know if extraction is necessary or if managing sebum and dead skin cells should come first. Since my skin tends to be dry and sensitive, I would like recommendations for a method that includes soothing care and can be performed without causing any irritation.