How can we re-train our 21-month-old to sleep in his own bed?
First, let me reassure you that you did not do the wrong thing. When children are sick or frightened, the vast majority of parents take them into bed. It's what your heart tells you and it is not wrong.
Merely plunking him in his crib and letting him cry until he throws up is cruel and counterproductive. If he was afraid before, he will certainly be now. Altering any routine that has been in place for a while should be a matter of small, gradual changes. Work out a game plan together that slowly moves him into his own room. For example, put a small bed next to his crib and one of you can lie down with him until he is asleep. Then start putting him into his crib with your hand on him until he falls asleep, but stay in the room. Turning on a night-light when you start your bedtime routine may become a signal to go to sleep; soon you can just turn on the light and he will become relaxed and drowsy. If you make changes slowly over a week or two he will be better able to adapt and you will eventually be able to leave him alone.