Eczema and under Eye Wrinkles
Wrinkles which are caused by eczema as opposed to age cannot be treated the same way. The most important things to do right now are moisturize, have humidifiers in your room, oral antihistamines when necessary. I cannot tell from the photo if Botox or Belotero would help you. Please find a board certified dermatologist with a great deal of experience in cosmetic and medical dermatology for the best results.
Dennie Morgan folds are lines under the eyes that are seen in people with eczema. Since these lines are not related to aging, they are difficult to treat. Oral anti-histamines (Zyrtec, Allegra, etc) can help with dark circles, a small amount of Botox in the lower lid can help soften the line (although Botox should be avoided if you get puffy eyes in the morning - it can make the puffiness worse), and Fraxel 1550 can improve the skin texture. A good eye cream can also help.