What are some good hair loss shampoos for oily scalps?

I have been very worried lately because my pre-existing alopecia areata has worsened since taking Maunzaro. Since I have an oily scalp, I have excessive sebum and waste buildup, which seems to be exacerbating my hair loss. Are there any hair loss shampoos specifically designed for oily scalps? What ingredients should I look for in a shampoo that is beneficial for an oily scalp? Also, my scalp tends to get quite hot, so would a specialized shampoo that provides a cooling effect or reduces heat be a good idea?