These days, every time I wash my hair, it falls out a lot. How do you take care of your scalp at home?

Hello everyone, I'm writing this because I was so shocked to see a bunch of hair piling up in the drain every time I wash my hair. ㅠㅠ I used to have so much hair that I would go to the hair salon to get it thinned out, but these days, I feel like the top of my hair is getting thinner, and I get really depressed every time I look in the mirror. I've been using all kinds of expensive products on my face, but I feel like I've been neglecting my scalp for too long, so I'm trying to start taking care of my scalp at home in earnest, but I have no idea where to start. ㅎㅎ;;

Everyone says that the basics of scalp home care are to thoroughly brush your hair before shampooing and to change your shampoo to a mild, slightly acidic, or functional one. Do you really feel that your hair falls out less just by changing your shampoo? Or is it more effective if you separately apply a cooling tonic or ampoule while your hair is still wet after washing it and massage it in with your fingers? I'm really curious. ㅋㅋ It's expensive and annoying to go to a salon to get a regular head spa, so I really want to know about a scalp home care routine that I can consistently do at home.

I have a hot constitution, so my scalp gets hot and oily in the afternoon. If you know of a tonic product that has a great cooling effect that is perfect for people like me who feel hot, please share the name. ㅠㅠ And I wonder if a salt scrub that I do once or twice a week is also helpful for scalp home care! If you have any real know-how or recommendations for strengthening the hair roots rather than the hair itself, please let me know. ㅎㅎ Have a rich and enjoyable day today, everyone~~