There is no need for an antibody test if you’ve been diagnosed by culture.
If you come off antivirals, you’ll develop antibody usually within 12 weeks at the outside.
It isn’t possible to know if you also acquired the HSV 1 orally without a swab test of the area you are concerned about. Generally, if a cold sore is going to develop, the tingling is in a specific location on the lip, correct.
If you want to reduce the risk of transmission the most, stay on antiviral medication.
If can’t accept this, then you should think about moving on. If he can’t handle this very minor medical issue, I hate to think about how he would handle something serious. And if he moves on to someone who actually does have oral HSV 1, they are far more infectious to him than you are with just genital HSV 1. infection.