Is it effective for acne treatment and suitable for skin that is not receptive to exfoliation?

I thought I needed to exfoliate because I had small bumps around my nose and cheeks, but my skin stung and turned red every time I used a peeling product, so I started looking into acne treatment.

My skin looks a little smoother the very next day after exfoliating, but after a few days, it becomes bumpy again, and my cheeks actually feel drier. I'm worried if continuing to irritate my skin is the right approach.

Can I expect acne treatment effects even on such sensitive skin?

I am wondering if I can reduce the exfoliation or manage it in a different way when treating acne if my skin is sensitive.

I would also like to know if there are cases where the condition of the skin barrier is checked first before acne treatment, and soothing or moisturizing care is started first. I want to minimize irritation as much as possible.