You don't mention the timing of the blood testing, which can affect a lot. Also, the igG blood tests can miss about 30% of hsv1 infections.
If you had a positive culture, then you probably have it. Cultures are known for false negatives, because of timing issues (like you mentioned). They aren't known for false positives.
If you get more symptoms, ask for a PCR culture. Those are more sensitive than a regular culture.
HOWEVER, ghsv1 is not that big of a deal, in the overall scheme of it. Ghsv1 doesn't often recur, it rarely sheds, and therefore, rarely transmits.
HSV 2 genital 15-30% of days evaluated
HSV 1 genital 3-5% of days evaluated
HSV 1 oral 25% of days evaluated
HSV 2 oral 1% of days evaluated
(https://westoverheights.com/herpes/the-updated-herpes-handbook/ - you should read this, as it has info about the testing and transmission. Much won't apply to you, so you can skip around, since hsv2 isn't relevant, but you might find it interesting.)
Also, many people already have hsv1 (about half the adult population, and it goes up to about 80% the older you get), so if they already have it, you can't give it to them again.
I hope this helps.