so Batman has the skill Functional Dissociation In Emergency that allows him to shut down all emotion when things get real bad which is why his coworkers think he's a sociopath and why his kids feel vaguely ashamed that they weren't born with this very impressive feat
yes there is a mini-little Bruce in his head that's having the panic attack and yes that Bruce comes screaming to the surface the second things are deemed safe and Batman has to go throw up in the corner in response