No. But the IgG test is not a perfect test, it misses 8% of HSV 2 infections compared to the western blot but without symptoms, I think infection for you is very unlikely.
It might be helpful for you to print out the CDC guidelines about HSV IgM testing.
Also, your doctor states that you are positive because you were exposed. But if you actually were positive by IgG, which you are not, it would be more than exposed – it would be infected. your doctor has a lot of learn about herpes.
Terri