It feels like I get more sebum around my nose when I only apply sunscreen.

I have been applying sunscreen every day because I was told it is essential to protect myself from UV rays, but strangely, on days I wear it, my nose and the sides of my nose get oily faster, and my pores feel clogged.

Especially in the afternoon, it looks like small bumps of sebum are rising around my nose, so I'm not sure if the product isn't right for me or if there's a problem with my skin itself. I can't go without sunscreen, so I'm using the lightest products possible, but it doesn't seem to make much of a difference.

In this case, should I cleanse more thoroughly, or would it be better to get separate sebum control treatments?

I am also worried that washing my face too vigorously dries out my cheeks. I am wondering if there is a skincare routine that reduces oil while minimizing the burden on the skin barrier.