A warm bath can give you relief from eczema. Don't make the water too cold or too hot. Try sprinkling baking soda or colloidal oatmeal in your bath to help soothe your skin. Bleach is even useful. Pour a small amount in a large bath, and it will help reduce the bacteria colonies that inhabit the skin.
Sweeping can cause issues with dust, and dust is not good for eczema. Vacuuming will keep the house clean while helping you to avoid flare-ups. While you have the cleaner out, head up to the bedrooms and vacuum the mattresses as well. This will help ensure that your room stays as dust-free as possible.