I'm not going to tell my gf some other girl I know recommended me for my future job
Do you think that was inappropriate?
I see no use of telling her that.
It's not good to hide things from your gf, even if it's small. If she somehow found this info out she'd be upset.
She doesn't need this information and that it's none of her business.
It seems silly to keep this info from her. I doubt she would care this much unless there was something going on between you two.