Is the collagen booster effective enough for pores with internal dryness?

I am looking into collagen boosters because I am concerned about my pores, but I am wondering if it would be okay for me to receive them since I have dry skin.

Right after washing my face, my whole face feels tight, but as time passes, oil starts to rise on my nose and my cheeks tend to stay dry and rough.

So, the pores around the nose are noticeable due to sebum, and on the cheeks, the skin texture and pores look rougher because the skin is dry.

If I apply too much moisturizer, my nose feels stuffy and greasy, but if I apply a light one, my cheeks feel tight, so it's hard to find a balance with home care alone.

Would a collagen booster be effective even for combination skin like this?

I am curious whether a collagen booster is different from a procedure that simply replenishes moisture, or if it is a method that also manages skin texture and elasticity. I would also like to know if it is better to manage hydration or the skin barrier before using a collagen booster if I have severe internal dryness.