False Negative on antivirals?

I was recently diagnosed with HSV2 in June by visual observation from my doctor. He wanted to wait a couple months to do the confirmatory blood test to ensure there wasn’t a false negative. I had a blood test yesterday and received a negative result today for both HSV1 and HSV2 but I am on daily antivirals. Could there be a chance of false negative since I am on daily antivirals? Is there anyway there could be another issue that may present itself similarly looking to HSV and I was misdiagnosed?