Not necessarily. When my cousin was little - under a year old - she was in a stroller, and two birds flew out of a pine tree right in front of her face, scaring her. She's been scared of birds ever since (and she's in her late 30's now).Oh trust me I'm thoroughly grateful that there was no more damage and very aware that it could have been his eyes or face. He is too young to remember so he shouldn't have a fear chickens thankfully. We hatched 7 chicks out this year for the first time since we had the roosters. I'd like to have chicks again in the future but I definitely could a new rooster later for that.
I think you know what you need to do with that rooster (or cockerel). Get rid of him before he does more serious damage to your little one. (And watch his current injuries for infection.)