Depends. May be helpful depending upon your climate. Eczema improves w a more moist environment. Asthma after worsens as moisture may breed mold which can irritate asthma. Appropriate medications are much more effective in general.
Humidifiers. Dry air often worsens eczema & asthma. As such, many patients find humidifiers (not de-humidifiers) to be helpful if they live with dry air. That being said, a too moist environment is not good since mold like to grow in overly damp areas. If you use a humidifier, make sure to clean the water reservoir in it regularly to prevent growth of mold in it.
Great for asthma. Dehumidifier - yes! Humidifier - no. Dry air in your home reduces populations of house dust mites, a major allergic trigger of asthma & eczema. Skin moisturizing is accomplished by bathing in warm water followed by applying creams & ointments (not lotions) to trap water in skin. Humidifiers increase dust mite and mold populations. They are only useful for brief periods for the treatment of croup.