Need recommendations for dermatologist for hair loss

Hello, in the past month or so my hair has been falling out like crazy and my scalp is itchy and dry so I'm thinking of going to a dermatologist to get that checked before it's too late and I end up going bald.

Do you guys have any recommendations for dermatologists or clinics that aren't too expensive in Tokyo? I know Japanese so it doesn't have to be English speaking.

And follow-up question, does the national health insurance cover these kinds of things?

Thanks in advance.

Edit: I live in Tokyo, forgot to mention that one my bad.

Edit 2: For extra context, the issue started after trying a shampoo for curly hair of the Shea Moisture brand but it hasn't stopped even after switching back to the H&S shampoo I was using before which used to make my hair look pretty dry and frizzy but at least I never had scalp or hair loss issues with it. So before trying any other products on my own and potentially make the issue even worse I'd rather consult with a professional.