When I have eczema flareups I will soak in a warm bath with vinegar, salt, oatmeal or baking soda.
Then I soak in the bath with those ingredients for around 30 minutes and do so every other day and eventually after a few weeks the eczema goes away.
After soaking in the bathtub and drying off you should apply a skin moisturizer cream to your skin which can help prevent future eczema outbreaks.
You should also use some OTC hydrocortisone which is what most doctors recommend for patients suffering from eczema.
Use the OTC hydrocortisone cream daily on the eczema and it should go away within a week or two.
If the eczema you have is more severe then it might take a month or two to fully get rid of the eczema.
Paying for some good eczema creams can help get rid of the eczema and prevent future outbreaks.