Good story, but your instructor should not have allowed you to take off
again after a bird strike.

Yeah, I was thinking the same thing! It is pretty risky to continue. If I
was in the similar situation, I wouldn't continue until I check the damage.
But, yeah, you had an interesting experience.

The closest thing I ever encounter with bird:

While at position and holding, I had to wait few minutes for the birds to
stroll across the runway.

By commercial, I experienced a go-around at short final. They made an
announcement afterward that they had to go around because a flock of birds
was getting in the way. I believed that was at Boston, but I could not
forget the look of white knuckle as the passenger (sitting next to me)
grabbed the armrest. It was a bit strange because the nose was actually
brought to the climbing position before you can hear the engine at the
maximum power. I tried to talk to that guy but, I don't think he was paying
any attention.

Toks Desalu
PP-ASEL
"Dyin' to soar!"