Genital HSV 1 is almost always acquired through someone with oral HSV 1 giving oral sex to someone who does not have HSV 1 anywhere. It is very rarely acquired through intercourse. I don’t know what kind of sexual practices you two are engaging in but if oral sex is involved, HSV 1 is possible.
The IgG test for HSV 1 misses 30% of infections compared to the gold standard western blot, so even a negative isn’t a perfect answer.
I would say you could consider redoing the IgG in 12 weeks or the western blot. In the mean time, if you get anything else that looks like a cut or ulcer, get it swab tested right away. The thing you described with pus sounds nothing like herpes to me.
Terri