Eczema and wrinkles
Eczema is very difficult because it is unpredictable and often genetic. Since Dennie Morgan folds are not due to aging, they do respond to typical anti aging creams or treatments. Some of my patients have had success with eye creams that contain caffeine, which shrinks blood vessels, but this will not help the crease very much. I have never found consistent treatment for Dennie Morgan folds, but a good non-sedating antihistamine (Zyrtec, Allegra, etc) can help with the dark circles and puffiness. Botox can help open the eye slightly, but it is risky in people with allergies because it can make eye swelling worse. Controlling your eczema is important, so I suggest seeing a dermatologist to control your symptoms. They can help!
Botox and fillers are not helpful for controlling itch and swelling of eczema
I am sorry to hear about your suffering and stubborn eczema around the eyes. Since you cannot be on topical steroids continuously, I would recommend that you try a holistic anti-inflammatory approach to controlling your eczema, and not Botox or fillers which have not been reported to be helpful for your symptoms. First, it is now recommended that those who have moderate to severe eczema ( as it sounds like you do) get tested for possible allergies with the allergist, as well as consider skin allergy patch testing with a board-certified dermatologist who does patch testing with the north american series. Once you have eliminated any obvious or less obvious allergens, then I would consider trying an anti-inflammatory diet and/or supplements with the help of pediatrician or allergist who is familiar with these supplements. For example, a dairy-free, low-glycemic (very low sugar), vegan diet is best. There are studies that show people with this diet have less eczema and psoriasis as well as other inflammatory diseases. Then I would add healthy anti-inflammatory supplements to your diet like aloe, bromelain, vitamin D, omega-3 and more.
Botox is not effective at treating eczema
Undergoing any treatment requires careful consideration of many factors.
When your skin is affected by conditions such as eczema, it is wise to undergo an evaluation by a board-certified dermatologist with experience in the particular condition.