Searching around the web, I found a lot of resources saying that baking soda (NaHCO₃) is good to relieve an itch. For example, this article Baking Soda for You Skin: Is It Safe, When to Use, and More
Baking soda is not a cure for eczema, but it may help relieve the itch associated with it. The National Eczema Association recommends adding 1/4 cup baking soda to a warm (not hot) bath and soaking for 10 to 15 minutes. Gently towel dry your skin and moisturize afterwards.
How does it work? I get that itching is caused by histamine, so does it simply reduces the histamine, or does it block the receptors, similar to how anti-histamine works? I tried searching for
baking soda itch review on Google Scholar, but there are no useful articles at a glance.