How can I add a system with a script, where if my enemy (skeleton/zombie) gets too close to me, a short scream will play and then I will die. How can I do this in Unity?
Add a trigger to your skeleton/zombie and then play an audio clip if the player enters the trigger.
As far as dying, you will need to make a very simple health script for your player where if your player enters the trigger you re spawn (from the way you are describing it, if the zombie gets close you just die, there is no actual βhealthβ).