This sounds like an allergic dermatitis and conjunctivitis. What I would suggest is for you to use cool compresses as much as you desire, but to also start using an allergy eye drop. OTC brands are Zaditor and Alaway; if these don't stop the itching, then you should ask your doctor for a prescription drop called Pataday. If the lid becomes red and swollen you may need to start using 1% hydrocortisone
ointment on the eyelid. If this is accompanied by fevers above 100.4 and you start to have eye pain, decreased or double vision then this may represent an infection of the skin and may require oral antibiotics which you would need to be prescribed by your eye doctor or PCP.
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor.