You don't need another test - your culture and blood test confirm the infection.
Some people just don't get a lot of outbreaks. You are one of them, apparently.
Herpes infects nerve groups, and genital infections infect the sacral ganglia. This means you can get an outbreak anywhere in the boxer short area, not just on the genitals, though that is most common.
I was diagnosed by a culture and a blood test. The cluster I had though was found on my back thigh so that had me doubting the result. I thought genital herpes was found only in the genital area. I was very scared that my husband now would think I had cheated when I have been 100% faithful. The test that came back stating I had herpes for a while now relieved him. How can I have only had one outbreak that I'm aware of? Should I have another test?
Nope, your daughter is fine. Herpes in a newborn can not be missed - the baby would be very sick.
How were you diagnosed with hsv2? Through a typed culture or blood test? Or did you have a doctor say "that's herpes, its genital, so its type 2"? Or a positive culture, with the same thought - genital = type 2?
Since you've only had one ob, I'd wonder if you had genital herpes type 1, which you can get if someone with oral type 1 performs oral sex on you. A type specific IgG blood test will determine this for you.