From kissing, there is no risk of hsv2. Hsv2 is almost always a genital infection, and herpes is only infectious from the site of infection. If you are infected genitally, you are only infectious from the genitals.
If the person has hsv1, there is a chance that you could get it, even without a cold sore being present. How high? It's hard to say.
Are you afraid of hsv1? That's a hard thing to be afraid of. Up to 80% of the population has it (it goes up as you get older), and if you are afraid of getting it from kissing, you might as well stop kissing people. Your parents may have it, your grandparents probably do.
You may have it and not know it. 90% of those who have it never get a cold sore. The only way most people know they have it is by testing. If you want to know, ask your doctor for a type specific IgG blood test.
Have you talked to your new friend about it? If you are becoming serious, at some point, things will progress, and and you'll need to have the STD talk. Don't be shaming or blaming - just talk. If you've ever had any sexual activity with anyone else, you could pose a risk to her as well as her posing a risk to you.
And please, if you haven't already, get help for the anxiety. There is help available, and you don't have to live fearing things like this.