Maybe some kind of scalp yeast/fungal infection?
I'm currently looking into Candida and fungal as playing a role in my POIS. I've had a long history of fungal problems.
Personally I've had decades of derma issues, fungal infections, itchiness etc. ex/ white blotches on my chest and back. I don't know what causes all these things. I used to have intermittently very greasy hair until I lost most of it, severe cystic acne (especially on my back) well into my 30s, still get acne occasionally in my 50s. Admittedly MPB and acne are considered fairly common. I could do without the fungal white blotches and the itchiness but for me, it's not the worst aspect of pois (if due to pois?). Maybe all these things are due to a haywire hormonal or immune system?
Re Candida, I explored that too. There seems to be quite a lot about that online but from what I've read, it's another of these things that seems to be hard to test for, that's supposed to get worse before it gets better (another "paradoxical reaction") etc. I used monolaurin and various other supplements for a while but it didn't seem to do anything much long term in my case so I abandoned that idea.
I would say Vit D3 has possibly helped me most with derma issues.
For a topical treatment I find ketaconozole shampoo works pretty well for skin fungus (which is what my doctor prescribed me).
I'm yet to try the OP's shampoo brand. Maybe he'd like to share the name of the brand with us?