There are a few possibilities here. One is that you have blepharitis, which is an infection of the edges of the eyelids right where the eyelashes come out. Blepharitis is usually provoked by chronic irritation of the eyelids, and it usually responds really well just to good hygiene and warm compresses to clean the surface of the eyelids. It is also important to stop using any mascara or other eye makeup until the condition clears up, as this is a major factor in bringing on blepharitis.
Another possibility would be that you have allergic conjunctivitis, or eye allergies, and that the allergies are provoking the itching and tearing on the surface of your eyes, which you are then interpreting as itching of the eyelids. Also, with allergic conjunctivitis it is common to have some eyelid puffiness. Allergic conjunctivitis usually responds well to the usual anti allergy medicines like antihistamines.
I suggest that you get in to see your primary care doctor
. Please seek help urgently if you have any severe symptoms, like puslike discharge from the eyes, eye pain, or fever
. These would be symptoms that the problem requires more aggressive medical treatment.