Some babies suffer from eczema when they are only a few weeks old. It should not be confused with dry skin, which is usually the same colour or just slightly paler than your child's regular skin tone, but feels slightly dry or bumpy to touch. For dry skin you need only moisturise (with a natural oil like olive oil).
Eczema tends at first to be dry, itchy skin that looks red. Sometimes the skin can get more inflammed or broken, especially if the itchiness causes your baby to try to grab at the areas affected. (At a very young age a baby will not be able to accurately scratch but may still grab, or rub the area against something causing it to be become more sore.)
Sometimes eczema can be caused by an allergy, but in the early months your baby is not eating foods and unless there are other signs of breastmilk allergy the best you can do is keep the problem at bay.

What can you do about eczema?
Use non-bio washing products, especially ones which are developed for sensitive and/or baby skin.
Do not over-wash your baby's skin but ask at the pharmacist or at your GP surgery for recommended alternatives to regular soap for bathtimes. (Some can be given on prescription to save the cost of expensive special treatments.)
If the skin gets 'angry' or crusty, see your GP, who may want to stay in touch and keep an eye on the condition.
Try to dress your child in cotton clothes that are not making her too sweaty. Do the same with bedclothes and avoid letting her get too hot.

Using medicated products
Your GP may suggest using a strong skin cream as some eczema will not clear up until you use a steroid cream. Not all have to be extremely powerful, but discuss the choices with your GP so that you are happy treating your child with something suitable to her age and condition.

For more about the condition in babies and older children, visit www.eczema.org.