How should I start managing sebum and pores around the nose?

Lately, sebum has been rising quickly around my nose, and my pores look much more prominent than before, so I am asking for advice on how to manage this. When I wash my face and apply my skincare products in the morning, it looks fairly clean, but after just a few hours, my nose and the sides become shiny, and my pores become noticeable again.

I thought I had oily skin, so I tried washing my face thoroughly, but if I wash too hard, the area around my nose feels tight or turns red, so I actually don't know how to manage it.

I have tried using pore packs and sebum-removing products, but they only make my skin look smooth for a short while before returning to its previous state after a few days, and it seems my skin becomes sensitive if I use them frequently. In this case, I am wondering if I should clear the sebum first, or if I should check my skin's oil-moisture balance and exfoliation condition first. I would also like to know how to manage both sebum and pores around my nose, as well as the typical frequency of treatments required.