I think you have to force yourself to think logically (it's what separates us from women) and then your emotions will balance out.
So, logically: think about how great your relationship is with your girlfriend and how much you love her. You want that to last, right? Well, you also know that if you do come off too clingy, if you're not letting her put in at least 51% of the effort, that the relationship will eventually end. You don't have to understand why or how, but you know from reading this site and perhaps your own life experience that this will happen.
Every time you resist contacting her, you are at the very least maintaining her attraction level if not increasing it.
Plus, it's going to enhance the time you do spend together. You'll have more to talk about. So the next time you have the urge to send her a text message about absolutely nothing or to call just to say hi, remember that by giving your relationship room to breathe you are doing it because you like her so much.