This is quite common and I feel like there is not a lot of info on the net about it. I see a few cases of these every month. My middle son has this problem. Itchy, red, scaly/flaky, swollen eyelids, mostly from allergies. The internet blames a lot of it on "contact" dermatitis...like being in contact with some chemical. But a lot of these are just from having simple seasonal allergies or skin allergy or even excema. In my experience it's not usually from some "chemical" that you got in "contact" with. The following is my personal method for treating this when I see it:
1) Benadryl Cream: cheap, OTC, readily available, VERY, VERY safe. Did I say "very?" VERY safe, even in children. My 1st choice.
2) 1% hydrocortisone cream or preferably ointment: also cheap, also OTC, also readily available. Not quite as safe. If used LONG term increases the risk of cataract formation and glaucoma. This of course does not mean that it WILL cause those, but it COULD. These need more supervision if a longer term treatment is maintained. For these reasons it's my 2nd choice.
3) Elidel cream: EXPENSIVE, Rx-only, but safe. This is my last resort b/c of the expense. It works, tho!
If you suffer from this ailment there are things you can do! Try not to scratch it (this is my son's big problem...he won't leave it alone), try to use gentile soap like baby soaps and hypoallergenic soaps on your face, and avoid "hot" compresses...if you're going to use a compress make it cool.