It isn't spicy, but the soup at Cafe Phillips on G is very good. Breadline also has great soup, but not sure how often it's chicken noodle. Whole Foods could do in a pinch.
You can call G Street foods to see what's on the menu.
Founding Farmers has a good tomato soup, but if you really want chicken noodle, it might not work for you.
I'll keep thinking. Hope you feel better soon, OP.