Hello, There is no doubt that this experienced affected you. However, after a traumatizing experience where you are faced with the idea of death, it is common to dwell on it. It forces you to deal with a fact that you have not yet had a chance to seriously and realistically think about it.
Feeling scared or depressed is normal after something like this, and if I were you I wouldn't be too worried. It hasn't been to long, and this may be on your mind for a while longer. But the more you think about it, the more comfortable you will become with the idea and it will simply become an experience. What you learn from this experience is based on your own perceptions and thoughts; thinking about the experience isn't the worst thing in the world.
If you truly feel that these feelings are becoming overwhelming to the point where they are unbearable, I would suggest talking to some sort of counselor. This shouldn't be something to become a major taproot into something bigger. That should be avoided.
As for your parents and family, you really don't know how they will react unless you tell them. Even if you slip it into a casual conversation, read their response, and judge whether or not you can delve further into the topic. This isn't something we want to repress and possibly cause further damage.
But in all honesty, I don't think it's much of a worry. It's natural to feel insecure or unsure about things after being faced with such an experience. Time will probably heal this one.
Good luck. :)
-MissLithium