I recommend a shampoo for oily skin during the rainy season.

Product Name: Kerasis Coconut Oil Shampoo

This is the shampoo I finally settled on after going from place to place as a shampoo nomad.
I have oily hair, and whenever summer comes, it gets greasy quickly. It was painful because of the smell from the top of my head, even though I washed it every day.
I've tried shampoos and hair vinegar that are supposed to be good for scalp odor, but the oil and smell still come up by evening.
In the meantime, a friend recommended this shampoo, so I gave it a try. After using it for about two weeks, I could definitely see results, perhaps because my hair's oil and moisture balance was restored.
The price is also excellent, in the low to mid-10,000 won range for two, making it great value for money.