Sesame Oil (herx)

I would say it isn't a herx but a food intolerance. I find it very hard to tell them apart I get almost the same reaction to a lot of foods I can no longer digest properly as I do when I am herxing - I feel very tired, headachey, cranky and ill. Your immune system copes better when you eliminate any foods or supplements that affect you negatively. I have very common foods that affect me now and the list is growing... coconut oil is one, ginger another, olive oil, and a whole lot of supplements. I used olive oil as a hair conditioning mask once and still got ill from it.
If it is a herx then you will feel better over time if it is a food intolerance then you never will.
A toxic overloaded liver and leaky gut syndrome are sometimes major contributors to these conditions. Other ways to deal with it is to go on the anti-inflammatory diet, eliminate all foods that compromise you and take supplements that reduce inflammation - omega 3, turmeric, Boswellia. Reducing all infections and parasites helps...but, sadly, as you can tell it is a complicated area.
Detoxing helps too - Dr Neil Nathan has a book called Toxic that is good in this area.