If the liver-flush is a trigger for your condition there is more involved than just oil. The cleansing process temporally alters the bacteria in your cut, reduces the electrolytes, changes the hormone and alters the cholesterol. Crucially it may modify the paths in which toxins are expelled so that more or less may be exit the body via urine or sweat.
The first step is to work out your triggers and avoid them. They may be food, pets, the environment, temperature, soap, cosmetics, etc. Make sure you wash your hands before you eat to avoid direct contamination.
People have some success with making sure they are the correct weight. Eat foods that keep them fuller longer and plenty of fresh fruit and vegetables, and oily fish such as salmon and mackerel.
We have a TV programme in the UK called the food hospital where people are treated with special diets to treat their condition and it has been successful with eczema and may also be good for you.
If you play the videos from where ever you live and have a good bandwidth allowance, this is the link: