u/No-Educator6046

I can't figure out if this is dry scalp or dandruff. My scalp is filled with stuff like this. I'm looking to buy Pilgrim's Tea Tree Anti Dandruff shampoo but I'm scared if it will worse the situation or make it better...

Whenever I scratch my scalp with my nails, there's this greasy residuals that comes out often on my nails. And my hair's been falling much since a few months. Anyone suggest any remedies or a shampoo which helps with this?