Obviously stuttering does hold up forming social relations . There is no doubt about it . Only way to socialize is by talking to people and we cannot express the way we want to without feeling embarrassed . So it’s a dead end . If your girlfriend is feeling bad about it then I wouldn’t say she is wrong. In my personal experience they can understand it as an excuse for a while but cannot do that for after a while . If you have to keep this relationship then you gotta go extra mile . Sorry for being straightforward about it .