Thank you for the reply and additional information.
If it is very close to the lid margin then it could be due to blepharitis
( inflammation of the lid) and can be treated with steroid+antibiotic eye ointment(prescription medicine such as tobradex eye ointment for a short period of 15 days, local application once at bedtime). However if the chapping is away from the eyelid margin and not very close to the eye then it could be due to allergic dermatitis/atopic dermatitis/contact dermatitis. The treatment is in the form of steroid cream for local application. Determining the exact cause would be ideal and would require a thorough examination by an ophthalmologist
/dermatologist.Such skin lesions can occur due to allergy to cosmetics/soap/contact with certain plants/airborne allergens such as pollen/chemicals in sprays and so on.
Since you have not got the desired relief inspite of taking oral anti-histaminics, it would be better to either consult an ophthalmologist ( as the part involved is close to the eye) or a dermatologist for a prescription of steroid ointment.
In the meanwhile keep the skin moist with the help of face moisturizers ( avoid applying very close to lid margin as it might get absorbed into the eye), apply cool compresses to get relief from itching.Use a hypoallergic soap and avoid use of cosmetics/cosmetic remover.
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Thank you and best wishes.
It was a pleasure to have answered this question.
Views expressed are for information purpose only and cannot substitute a visit to an ophthalmologist