Supposedly this is die off of bad bacteria, candida etc...

My body literally rejects coconut oil. If I put it in my mouth I get so nauseous that I can't swallow it. Even if I smell it I get nauseous.

Yes definitely. I think it's good to incorporate it if you can, just start with very small amounts and gradually increase. Most likely your body will get used to it. I take about 4 teaspooons per day but I had to build up very slowly.

How much coconut oil did you have? You really do have to gradually build up your amount, or you will have terrible detox symptoms. I take about 3 tablespoons a day, but I had to very slowly build up the amount. About 4 different occasions I had the exact same reactions you did, but that was because I wasn't pacing myself enough.

Could be a food sensitivity ?

Just a suggestion. you may have already know this or checked into all this. Regarding coconut oil, I suggest making sure it is certified organic coconut oil that is NOT processed in a factory that processed PEANUTS or even tree nuts. The labels will NOT always specify this so I recommend calling the manufacturing company. One company stated they do process peanuts and tree nuts in their factory yet it is in a different part of the factory plus they even clean their processing machine that processes the coconut oil with coconut oil YET I did not wish to take any chances using their product.
Peanuts can be grown in soil that contains the fungus aspergillis.
Anyone with adrenal fatigue should avoid peanuts......not only because of the oils being rancid but because of fungii in the soil. A peanut allergy/sensitivity may actually not be a true allergy/sensitivity to peanuts but to aspergillis.