Does sunscreen have an acne treatment effect on the small bumps that appear after applying it?

I apply sunscreen every day, but on some days by the afternoon, the sides of my nose and the inside of my cheeks feel stuffy and I get the sensation of small bumps forming, so I am looking into acne treatment.

I absolutely have to protect myself from UV rays, so I can't stop using sunscreen, but sometimes the results are similar even when I switch products, so I'm not sure if it's an issue with my skin's sebum or my cleansing routine. It's difficult because if I wash my face too vigorously in the evening, my cheeks get dry, but if I wash gently, it feels like residue remains.

Would acne treatment be effective in this case as well?

I would like to know if I can consult with you to determine whether the clogged pores during acne treatment are caused by the products or my skin condition. I would also like to know which type of sunscreen or cleansing method is less harsh after treatment.