My boyfriend: porn addiction or pedophile?
It depends. If the images on his computer are of actual underage girls and not just women made up to look underage, then by definition he is a pedophile. (Personally, even if the girls are of age and are simply made up to look underage, I think your bf is a sick bastard, but that is a personal opinion some others may not share.) If it is apparent that the girls are actually underage, then it would be my hope that you would contact the police and turn the sob in. But I would suggest you be pretty sure that is the case.
I will assume a porn addiction and will only say that if his behavior is not something you wish to put up with, then you need to talk to him about it. And if he does not change, then you will have to decide if you can stay with someone who seems addicted to porn. Only you can make that call.