I agree with the previous post, you have nothing to be concerned/worried about as far as your health.
I don't know which Liver Flush protocol/recipe you're following, but apparently it's one with TWO major doses of olive oil. And if you're a first time flusher with a congested liver and gallbladder, your report of nausea and non-digestion of the olive oil is something that makes sense.
We take the ES to cleanse the bowel AND more importantly to loosen/relax the biliary ducts, so that when the major amount of bile 'hits', the build-up in the ductwork will come out easier. What actually causes the major amount of bile to happen (that flushes out the stones and build-up) is the olive oil.
The liver is responsible for processing fats, and so when the liver is told by your mouth and stomach that there's a HUGE amount of fat on the way, it goes into major production of bile so it will be able to process all the oil (*see next paragraph). That extra bile is what is responsible for the "flush". So if your liver/gallbladder are on the congested side (which most are), then the first dose of olive oil probably got 'digested and dealt with'...but a second major dose the next morning might have been slow to leave the stomach, because the liver was just exhausted from all that major activity the night before and needed some time to recuperate before producing another huge batch of bile. At least, that makes logical sense to me :)
* This is why one can still have a successful flush, even if the oil is vomited before it has a chance to digest. Just the knowledge that the oil is on the way to be processed is enough to trigger the liver into major bile production, so even if it comes right back out, one still succeeds at cleaning stuff out of the liver & gallbladder. Also to keep in mind, some first time flushers that are symptomatic (have gallstones, pain, liver sensitivity,etc.) are so clogged, that when they drink the olive oil mixture, they immediately throw it back up. I've read this is because the liver is SO clogged, that the body knows that it can't possibly process all that much oil at once, so out it comes. But even then, the liver still produces major amounts of bile and starts to flush things out. Isn't the human body miraculous?
When you did the SWF, did you use "normal" salt or Sea/Celtic/Himalayan salt? If you used normal table salt , that is probably at least part of the reason for your nausea. And even if you used healthy salt, many people become nauseated when they do a salt water flush, especially when their system isn't used to it. I'd advise (next time) to lower the amount of salt you put in the water, or increase the amount of water, so there's not such a strong impact.
You just had a GREAT flush (overall) and you're doing wonderful things for your body. The fact that you're still feeling 'very ill' at the time of your post, could have been from that second dose of olive oil, too much salt (or the wrong kind) in your SWF, or a combination of both.