You seem to have done a lot of research on your own and to that I say, "Good for you."
I don't know if you know that HIV dies 30 seconds to a minute after it leaves the body. The kind of cleaning that they did in the place you mentioned seems to me that the HIV is dead. Especially the flame part.
I live in Canada and when I teach I tell my audience to have their tattoos done here where it is safe instead of a place far away from home. Here you can ask to see new ink being opened, new needle etc.
That's my addition to what Homerx my educated friend has said.
If you are getting frustrated, let your wife get tested for HIV and Hep C three months from the supposed point of infection. Then you too would have to be tested if you are having unprotected sexual relations with your wife!
Hep C can live on the surface for about 6-8 weeks and I think the flames would kill it.
Again, instead of driving yourself crazy, get the tests done. You did not mention when the tattoo was done.
Always
Muthoni (Mson)