Well, generally speaking, you should know that when you get eczema around your eyes, it can causes red, itchy and inflamed patches, and then it may swell. In common, eye infection can be the most common cause of eczema. And according to some researches, when eczema occurs on the eyelids or the area around the eyes, you should avoid rubbing and scratching which can lead to potentially serious infections. To treat it, you can use cool compresses to your eye area to relieve discomfort and itching, and also it can reduce swelling. Also, you may need to go and have a testing.