So sorry you got sick. =( I have too while doing LF. I have thrown up a lot- 4 hours after I took the mixture-and later in the day started expelling plenty of stones. Give it some time. I didn't fight the nausea or need to use the rest room.
You are not alone. This happens with lots of us. Let us know how you do. And remember it's an option to take a colonic the next day or so to get out any thing the Epsom Salt didn't. I'm sure you already know that, just throwing it out there.
Just read the part about your prep...were you able to do the full prep? Unfortunately, If you didn't prep with the apple juice or Apple Cider Vinegar and organic food for at least 5 days- this may not be a successful flush. But I really hope it is and works out beautifully.