For those of you with problematic oily scalp, how do you take care of your scalp at home?

My face and body can get dry depending on the season, but my scalp is oily all year round. Aside from my hair getting greasy quickly due to the oil, I haven't had any major issues. But lately, my crown has been itching and I've been getting pimples. When the pimples burst and heal, I can feel the scabs on my fingertips.

I'm worried that my scalp condition could lead to hair loss, and I need to start paying more attention to scalp home care. But honestly, I've never really taken care of my scalp, thinking that just washing my hair regularly was enough. Now that I'm thinking about starting some scalp home care, I'm not sure what to do.

When I wash my hair, I soak my scalp in warm water, then lightly shampoo once, then shampoo once more, thoroughly rub my scalp with my fingertips, and rinse it several times, being careful not to leave any residue.

I mainly use deep-clean shampoos that are good at removing oil, and I rarely use conditioners or treatments because they make my hair feel greasy.

If I want to do scalp home care, what should I change and what should I add here?

For those of you who have oily scalps and breakouts like me, I'd appreciate some advice on how you do your scalp care at home. It would also be helpful if you could recommend some helpful products.