Fell on my face and awoke with a scar
Another mistake living deep in my heart

from Kendrick Lamar – Bitch, Don't Kill My Vibe Lyrics on Rap Genius

As a young man, Kendrick had to pay for his mistakes. When he screwed up, he was left with permanent physical or emotional damage to remind himself of it.

This may be alluding to being sensitive, more sensitive than he thinks he should be.

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