There are over a hundred of different strains of HPV around, and if you've been getting warts on your hands for years, then you've already had at least one strain of HPV for years, and since this latest round seems to be different, it's probably a different strain. As far as getting a genital strain of HPV from your gf, since you've already been sleeping with her, you've probably already picked up anything you're likely to get from her. HPV is very easy to transmit, the odds of her having a strain and you haven't picked it up by now are very slim. However, if you have picked anything up from her, it would have nothing to do with the warts on your hands. Genital warts grow in the genitals, plantars warts grow on the souls of the feet, etc. Basically, different strains like specific environments.
As far as what's in your mouth, I don't know anything about canker sores or cold sores (herpes), but I'm pretty sure they have nothing to do with HPV. Does she have any problems with her mouth?