They usually do not throw up, but a little water can come out just after drinking if their head is down. Did you accidentally squeeze her crop when she threw up? Pressing on a full crop when holding or lifting them, can cause contents to come back up. I would feel of her crop now, and then again in early morning before she eats or drinks, to make sure that it is empty and flat. I like to keep my sick hens in a wire crate with food/water inside the coop and run with the others, so they can see each other. So she probably would enjoy getting outside. When they are away from their flock for more than 3 days, they may be pecked or bullied. So visits each day may help prevent that.
