How should I deal with localized dead skin cells on my face?

I usually use a moisturizer quite well.

However, as the weather has recently gotten hotter and the sun has gotten stronger, I increased the amount of sunscreen I applied, and as a result, I found myself cleansing my face more thoroughly.

Some time later, I noticed that dead skin cells were forming and the skin was peeling particularly between my eyebrows and on my temples. How should I manage this?

I have a strong urge to keep buying scrub products and scrubbing hard, but I'm also worried that I might just make things worse by scratching myself.

It's not like my whole face is flaking; only specific areas are severely peeling. Could this mean my skin type has changed to combination?

I used to have oily skin, but recently it has turned dry, so I am a bit surprised.

How should I manage this in my case?

I usually double cleanse using oil and foam cleanser, and I am wondering if it is okay to continue using the same cleansing routine.