I found this on WebMD.com -- sounds like the best thing to do is to just rinse your babies skin with water --don't use a brush or wash cloth which may be irritating the skin more -- then, pat dry and apply a lotion.
Hope this helps -- see below.
What Are the Treatments?
Good skin care is a key component in controlling eczema. Proper care of the skin can often be enough in many milder cases of eczema.
In treating eczema, most doctors will start patients on basic therapies. One example is a room-temperature bath to remove crusted skin. A good moisturizer (in cream, lotion, or ointment form) helps conserve the skin's natural moisture and should be applied immediately afterward.
If mediation is needed, newer drugs called topical immunomodulators are available to help treat eczema. These medicines help control inflammation and reduce immune system reactions when applied to the skin. Examples include Elidel and Protopic. Use of these medicines may help reduce the need for corticosteroids.
WARNING: The FDA has issued its strongest "black box" warning on the packaging of Elidel and Protopic. The warning advises doctors to prescribe short-term use of Elidel and Protopic only after other available eczema treatments have failed in adults and children over the age of 2.
Research in animals has linked Elidel and Protopic with an increased risk non-Hodgkin's lymphoma. In those studies, the risk of cancer increased as the dose of the drugs increased. The FDA has also received reports of serious adverse events in children under the age of 2 who were prescribed the drugs, although they have not been approved for use in children in this age group.
Corticosteroid creams and ointments have been used for many years to treat eczema. Your doctor may recommend application of over-the-counter hydrocortisone cream in mild cases but often will prescribe a stronger steroid cream when the eczema is more severe. When other measures have failed, the doctor may prescribe oral corticosteroid medication; steroids should always be taken with caution and never without medical supervision.
Taking oral antihistamines may also help relieve symptoms. Some of these may cause drowsiness, which may be of benefit if nighttime itching is a problem.
For extreme cases of eczema, therapy using ultraviolet light may be prescribed. In adults, drugs that suppress the immune system may also be an option in the more severe cases. These medicines, such as cyclosporine or methotrexate, may be used in cases when other treatments have failed.
To relieve stress and improve circulation, it also helps to take a brisk walk or exercise on a regular basis. Set aside time for other relaxing activities.