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You have Seborrhoeic dermatitis
. Squamous blepharitis
is what you have on your eye lashes and eyebrows, which is again a manifestation of seborrhoeic dermatitis. Use an anti dandruff shampoo with ketoconazole
2% and ZPTO 1% three days a week for scalp. A baby shampoo can be used to clean the eye lashes and eyebrows. An antifungal cream like ketoconazole 2% twice a day will help to decrease your skin rash
as well. If it is still not coming under control, please see a dermatologist
.It is better to avoid applying oil on your hair as the fungus which cause this rash feed on oil.
Hope this helped