How do you manage scalp dandruff?

I'm worried because my scalp flaking has gotten much worse lately. I have dry skin to begin with, but maybe because of the change of seasons, white flakes start appearing less than a day after I wash my hair, and sometimes it even itches. It really bothers me, especially when I wear dark clothes, so I get stressed every time I look in the mirror.

I use a mildly acidic shampoo and tend to wash my hair about every other day. However, the dandruff hasn't decreased, so I'm wondering if I might have some bad habits.

I've been searching lately and found that there are many scalp scaling products and shampoos specifically designed for exfoliation.

There is so much talk about how tea tree oil is good, how products with salicylic acid are good, and how massaging with a brush is best... but I honestly don't know what to use. I'm also worried that using just anything might make my scalp even more sensitive.

If anyone has similar concerns, could you please share what worked for you?