Oh, so you tested negative for HSV 1 then. the IgG test for HSV 1 misses 30% of infections compared to the western blot. You symptoms sound like they could be HSV but negative swab test seems like the lesion was not herpes.
You could ask her to go on suppressive therapy sure. But if you decide not to be with her because of this, the next person you date may be infected but not know it and tell you they don’t have it and then get infected from someone with asymptomatic infection. But your call. I think this criteria for choosing a life partner is pretty questionable, given the high prevalence of this infection, but your call.