I might also add, there are no such tests for low risk hpv. Only high risks which is the ones that cause your cervical cells to turn abnormal. They test for the high risk strains. You won't know you're the carrier of low risk strains (6-11 strains usually cause warts) unless you become symptomatic. Then only way to tell is to have the lesion removed, then sent to pathology for verification. Only then you'll know for sure your lesion is a wart. But most dermatologist will know if it's a wart by looking at it. It's their field. They can spot one from a mile away.
1: genital warts erupt directly from the skin.
2: skin tags have a stalk so they don't pop directly from the skin. Think of it like a tree. So skin tags have a stalk and warts don't. That's the difference between those two.
This is difficult for me to figure out since you didn't mention dates of when you were tested vs when you saw your GYN but I am going to guess.
You should also understand that a negative test result may not definitively mean you don't have it. The virus never goes away yet women can get negative results after a positive result. There is only one explanation for this. The test that women can take cannot reliably detect the virus because the levels may be too low at the time of the test.
You should always go see a dermatologist for any skin issue. If warranted, your dermatologist can remove one and send it out for a biopsy. That is your last option to know what they are or aren't. Visible inspection by your dermatologist may be enough. They are trained to differentiate between tags and warts. Go see your dermatologist and let us know what happened.