Well, if your eyes have eczema, red, itchy and inflamed patches may occur. And in some cases, it may swell. For the causes, eye infection can be the most common cause. To get rid of it, you can apply cool compresses to your eye area. For example, you can use some ice. In that way, it will relieve discomfort and itching, and also it can reduce swelling. By the way, you can use a small towel with cool water and apply it to your eyes for 15 to 20 minutes as needed. 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. Anyway, just be careful.