From OP's perspective, as a man, he didn't think rumor about he having sex with a woman is a problem (if it's a gay rumor he may react differently). But from many women and some misogynic society perspective, rumor about woman having sex with a man still make women feel uncomfortable since many people may view said woman in degrading way, as if she's 'used' by said man or 'easy' while view a man in rumor as 'macho' or 'player'. Even in modern society or between youngster, these mindset still ingrained in so many people.

So, OP's girl friend being pissed when find out about the rumor is the reaction that can be expected and it's OP's fault that even he have time for a month he didn't try to stop it or clarify things.