Neither answer is the best in this context, but B is more likely. The thought would most likely be expressed as:
I was nearly hit by a car, but luckily I managed to get out of the way.
To begin to answer your question simply, let me remove some of the context to make two simple statements:
1: I could have been hit by a car.
2: I might have been hit by a car.
Both of these can be used as statements of past possibility. 1 is about a real possibility. 2 could be used in exactly the same way as 1, but it could also be a speculation. That is, a possible explanation of what happenened. Let's add some context again to illustrate this:
A child has just run into a busy road to collect his ball.
Mother: What do you think you're doing running into the road like that?! You could have been hit by a car!
A man wakes up in hospital with cuts, bruises, and broken bones. He has no memory of what happened to him.
Man: Doctor, what happened to me?
Doctor: We don't know. You might have been hit by a car.
