Yes, it's conclusive.
It can take up to 90 days to develop antibodies, but most people will by 6 weeks, and since you had symptoms, you probably would have, too.
A syphilis sore would take at least 3 weeks to appear, and would last about 3 weeks, not 8 weeks. It's not herpes either - a herpes sore wouldn't last nearly that long.
Has a doctor actually seen this?
Google molluscum. It doesn't sound exactly like what you have, at least as I imagine it, but take a look. If it is molluscum, it's not from this encounter, as the incubation period (time from infection to symptoms) is usually at least a few months long.
The person I had unprotected sex with was a woman in her 50’s if that matters at all.