The portion "I grew afraid" is correct and usable in written English.
It can be used when someone is expressing a feeling of increasing fear. For example, "I grew afraid as I heard the thunder booming outside."
And so I grew up afraid of racists.
I grew to be afraid of it.
I told you that I grew up being afraid of Thomas Quick.
While I was waiting for him to call, I grew more and more afraid that he'd get angry at me for wasting his time with piffle.
I grew more nervous and afraid, especially when the guy in the passenger seat said, "I hate working with the whites," or rather he used the word "Moors", which made me believe that they were waiting on a Mauritanian team.
"I've begun to grow afraid — so awfully afraid — of the young," he says).
I'm not afraid of pop music, I grew up on it.
I grew up without a fireplace because my neurotic (but fabulous) parents were afraid of fire.
Though I grew very large, though I developed great capacity of mind,I was afraid of my mother.
