A large red patch on back scalp & neck.

I'm experiencing itchy scalp from more than 6 months. It looks like scalp psoriasis on the back of my scalp end & neck but i'm not sure what is it. There's a red and purplish patch which itches a lot and is increasing as I have peeled off the skin due to itching. It's also causing a lot of hair loss. My hair were thick and now they have become too thin and rough. It feels rough when I apply anything on it. If i scratch it then blackish skin comes out. I've been applying aloe vera gel and coconut oil but it didn't made any difference. The affected area has increased and it keeps increasing. Reaching scalp its removing hair from that area which don't grow. The first picture is of 2 months ago. Second picture is of this month (hair got removed from scalp as the affected area increased). Please help.