It's very important to stop scratching. Scratching only further damages the skin, and it causes repeated eczema episodes at the same spot where the skin was scratched. I know it feels good to scratch the itch, but scratching is very destructive in the long run. Here's an article on how to stop the itch:
The article's suggestion of putting crushed zinc tablets on the eczema sounds promising, although I haven't tried it. Aveeno makes a colloidal oatmeal mixture for the bath that works similarly to the article's suggestion of putting actual oatmeal in the bath.