Eczema herpeticum is not common at all. When you consider how many people have herpes cold sores and how many people have eczema, you would expect that there would be many cases, and yet I can't remember the last time I saw a case in an adult. I would advise that you avoid kissing your girlfriend if she has an active attack--which I assume you would do anyway. If you develop a widespread rash with blisters and fever, a doctor could treat you, but again, that's really not likely.
As to your second question, herpes doesn't generally affect the inside of the mouth. You should ask a dentist or dermatologist to look inside and see if your guess about biting your mouth is correct, as it probably is.
Best.
Dr. Rockoff