HSV1 is generally responsible for oral herpes, and HSV2 is generally responsible for genital herpes. HOWEVER, you can get HSV1 in the genital region, and HSV2 orally. The nice(r) thing about this is that the virus won't usually act as strongly outside of it's home turf. This means that symptoms may be milder, and likely won't reoccur. If you have not been tested for herpes I suggest you visit your health care provider and find out which you're positive for.
There is a possibility that she can spread genital herpes to you, even if she is asymptomatic. I know condoms
suck, but try to use them every time you have intercourse, and especially during an outbreak if you're still going to be sexually active (which isn't wise).
In terms of self-transfer of the virus, yes, yes you can. If you touch your sores and then touch your genitals, or if you masturbate using saliva for lubrication, you can put yourself at risk for a genital HSV1 infection (assuming that's what you have). Women are more likely than men to acquire genital herpes, but you are still at risk.
If your girlfriend is not on something like Valtrex, perhaps talk to her about it if it's financially reasonable. This will limit her outbreaks, shorten their durations, and also prevent genital herpes transfer to you, the partner.