No, the casing that is ejected is usually brass of some sort, the bullet is sometimes clad in copper like this one. Utterly frightening story, glad no one was injuredI'm not from the USA, so I don't know much about guns, but...
Isn't the copper cylinder the casing of the bullet? Wouldn't it be (usually) found near where the shot was fired?
Anyway, I'm glad you were unharmed.