I'm curious about scalp sebum care for late autumn.

I wash my hair every other day or every day. I am concerned because my hair gets oily easily, yet feels dry and brittle. Although it is not very visible in the photo, I have severe dandruff despite washing it frequently. My scalp also itches often. Is the shampoo the problem? I currently use a branded product from a major company sold at the supermarket; should I switch to a better shampoo? I am also looking into scalp boosters due to my scalp concerns. I am not worried about hair loss, but because my scalp has excessive sebum and my hair is dry and brittle, I am considering getting a scalp booster (Pantodil) treatment. Has anyone tried scalp care during the autumn season? I would also appreciate shampoo recommendations.