Red, dry skin on eyelid

[CherryBakewell]

My two-and-a-half year old has red, dry skin on one eye-lid (a tiny bit also on the other eyelid). A few months ago she started having a typical red rash reaction to tomatoes/peppers/eggs/crisps, which we now avoid, and the rash has gone. On the advice of homeopath we also avoid cows milk. Has anyone else had this type of problem? Is it linked the the chin rash?

(Forgot to say) Her eyelid doesn't seem to be sore or itchy.

DS has dry/red skin on both his eyelids but he has eczema. When we have been to the GP they always say that is what it is but he had some Fucidin cream once which did work a bit but they are itchy as well and he rubs them quite a bit - but it does come and go though, so I am not totally conviced it is to with his eczema.