Since you took the test 11 days after the encounter, it was too soon for it to be positive from that encounter. This means that you had it before that time.
This is probably a long-established oral infection. Many people get it as kids from family members who kiss you.
Unfortunately, with an index value this high, it's not likely to be a false positive.
Yes, it's possible to transmit when you kiss someone, or when giving oral sex, if someone doesn't already have hsv1 antibodies. (About 2/3 of adults globally have it, about 50% in the US do. 90% will never have symptoms.)
You are not contagious from your genitals.
The person you are going to go see - you need to ask about test results, because remember that even though you are afraid of telling her about hsv1, she might have something else you could be at risk for.