Eczema is partially a problem with liver toxicity, and partly allergic response. Stress increases the problem due to weakening of the adrenal glands.
The best way to cleanse the liver is with digestive bitters. These are bitter tasting herbs that when they come in to contact with the tongue they stimulate the bitter receptors. This in turn stimulates the vagus nerve, which causes the liver to flush. You only need to taste the bitters to work, so I recommend 1/2 dropper full on the tongue several times a week. Drink a lot of water throughout the day when using bitters.
As for the allergy component, allergies result from poor adrenal function. A lack of antihistamine and anti-leukotriene epinephrine, and lack of immune modulating and anti-inflammatory corticosteroids lead to allergic responses. To build up the adrenals you need vitamin C and pantothenic acid, the two most important nutrients for the adrenals. Natural vitamin C sources are the best such as watercress, kiwis and berries. Adaptogenic herbs also help to strengthen the adrenals. Some of my favorites include schisandra berry, licorice root, ashwagandha, jiaogulan, astragalus, Siberian ginseng and suma.
Remember to stay away from stimulants like caffeine.