Usually, false positives is when you have higher risk sex (unsafe sex but not always) with partners who have multiple partners or when you yourself have multiple partners and when you test too soon after your last exposure. I've seen some suggest on here 8 weeks after last exposure and some say 10-12 weeks after the last exposure. If that second test (at the 8 week or 10-12 week mark) is still positive, you don't have to test again. Unless you want to get the Western Blot test which is the better test.
I am in the same boat. No symptoms, positive result, But I tested too early. I must re-test at the better time and stay celibate for a few months. What I don't understand is if I do get a second positive result and still have no symptoms, if I can get on the meds to reduce the transmission chances or if I have to wait until after an outbreak occurs to get on the meds. I'm going to ask my urologist soon about that.