From what you write, I'm not sure whether the red lines are anything more than scratch marks, so I wouldn't rush off for laser, because these marks fade themselves if you leave them alone. As to why you're so itchy, I'm really not clear--eczema can cause itch, but there would be a scaly rash, and there doesn't seem to be. I advise you to get an over-the-counter anti-itch lotion like Sarna, use it whenever it itches, and see a doctor for proper diagnosis.
Best.
Dr. Rockoff