I would go with the culture result, as those are more accurate than the blood tests, though if you are wanting confirmation, you can take a western blot test.
Did the culture actually say hsv2, or did they just say hsv2 because it's genital? If it is type 1 genitally, it's not uncommon to not get another outbreak after the initial one, and the IgG misses about 30% of hsv1 infections.
Can you get the results of the culture and make sure it was typed?
You can read more about getting a Western Blot here - https://westoverheights.com/herpes/getting-a-western-blot/ or here - http://depts.washington.edu/herpes/pages/frequently_asked_questions#faqCat-4