This is such an unusual case. The swab tests are very rarely wrong and especially when they are also typed.
I think if I were you, I would wait and do an IgG test in about 6 weeks and see what it shows. It’s a shame you don’t have a baseline antibody test, showing that you were negative.
It is possible that he has genital HSV 1 and you acquired it through unprotected intercourse.
It is also possible that you have molluscum in addition to HSV. Syphilis to me seems extremely unlikely but a blood test for that will give you the answer you seek.
Terri