Almost certainly these skin conditions will affect hair growth. However, in the end, it is the inflammation associated with the skin conditions that causes the hair loss.
When inflammation occurs in the skin, small proteins called ‘inflammatory cytokines’ are released. This is beneficial for healing wounds. However, some cytokines quite literally block hair growth. If those cytokines remain present in the skin for a prolonged period, the hairs will not return to the growth phase of the hair growth cycle: They will shed and not regrow again.
However, there are several known ingredients that inhibit inflammatory cytokines and increase ‘growth factors’, which are proteins that keep the hair in the growth phase and prevent shedding.
By reducing the inflammatory cytokines that prevent hair growth and increasing the growth factors that keep the hair in the growth phase, gradually the hair may return to normal.
In cases like yours where the hair loss seems directly linked to inflammation, using something like the Growth Factors serum is probably the best approach.