Thanks for the query.
Dry patch in pubic area is unlikely to be eczema
The patches of eczema usually ooze.
It might be a fungal infection
known as tinea cruris
You can try an anti fungal cream.
Remember to apply the cream for atleast 1 month even if the lesion disappears.
This will help you.
If you dont get relief in a week, you must meet a dermatologist