It is better to follow those schedules to T, especially when you are so sensitive.
Try to drink the Oil+grapefrui jice mixture through a straw.
One more thing that works perfect for me when it comes to keeping this drink down: (even though the recipe says to lay down)I try to stay vertically for about an hour after drinking it (at least esophagus has to be vertical, you can seat or lay on a bunch of pillows), it helps to burp the air out. When you lay, a simple burp can make you throw up.
You can still expect some results tomorrow, just watch your stool carefully. There were some posts saying that some people flushed some stones by just rinsing their throat with oil, it sort of gave the gall bladder a signal to release bile to digest a lot of oil, and that bile flow flushed the stones out. It may happen in your case too. Just don't forget to post your results whatever they are.
If you want to do another flush, you can do it in a couple of days I think. Just don't eat fat food and follow the recipe.