According to a song called "Running Scared" .
"i’m running I’m scared tonightI’m running I’m scared of lifeI’m running I’m scared of breathing." What does "I'm running" means in this situation?

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that means i'm running away from what i'm scared of.
“我要逃避”的意思！

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scared of breathing :
is the guy running away from some disaster that caused pollution (contaminants) 
in the environment (notably in the air) ?

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Here's a song by Roy Orbison called Running Scared
http://www.youtube.com/watch?v=s9SgtpkpPS8