I have inner dryness; is it okay to use matte cosmetics?

My skin is dry on the inside, but the T-zone is oily; that is my skin type.

So it feels shiny, but deep down it feels tight...

Can I use matte powder or foundation with this skin type?

Also, in the summer, if I apply something too moisturizing, it gets greasy and breaks down quickly.

Which product should I use to ensure good longevity without dryness?

I am curious.