Dust can cause issues. Rather than dry dusting, use a damp dust method instead. This will help capture the dust, rather than simply spreading it around the home. Also, because rugs and carpets are a beacon for dust, try not to have them in the house if at all possible.
Make sure you wear clothes that are comfy as possible. People that have eczema have skin that is very sensitive to certain fabrics. Try sticking with clothing made of breathable fabrics like cotton or cotton blends. Try to avoid wearing synthetic fabrics or wool since these materials can cause flare-ups.