Do not scratch your eczema. It is hard to resist because eczema is an itchy skin condition, but scratching makes it worse. You can increase the itching, damage your skin, and increase your risk of getting an infection. Try keeping the skin moisturized, bathing regularly, and using cold compresses to alleviate itching.
Use an antibiotic ointment on severely cracked skin. This can prevent infections from forming. It also serves as a moisturizer. Do this sparingly though; prolonged use of antibiotic ointments can render them ineffective. If you do have an infection, you should consult your doctor, who may give you an oral antibiotic.