Exfoliating makes my skin more sensitive rather than smooth.

I used an exfoliating product because the skin on my nose and cheeks looked rough, but instead of my skin becoming smoother, it would sting and cause small breakouts the next day, so I have stopped using it recently.

I tried to manage my skin because I heard that dead skin cells clog pores and cause bumps, but now I'm worried that I might have just irritated my skin barrier instead.

However, if I do nothing, sebum builds up on my nose and fine bumps appear on my cheeks, so I do think that some care is necessary.

In this case, would it be better to gently smooth it out with a skincare routine rather than removing dead skin cells directly? I am wondering if there are sebum and dead skin cell treatments available for people with sensitive skin. I would like to know how to manage the condition to prevent clogged pores while minimizing irritation.