Do you have history of oral sex with someone who has HPV? Based on info I have read, its hard to contract warts orally. The only strep like infection someone could contract through HPV is more likely a baby passing through the birth canal of a mother who has warts. Typically, if you express this concern to your doctor, a throat culture can be taken to determine the cause of your sore throats. My guess is that its not related to HPV.
I have read that the symptoms of warts in the throat are most likely to be trouble breathing, or making a strange noise when you breathe. Warts are usually painless so I don't see how it would cause a sore throat.
So, what is your question?
My persistent sore throat turned out to be related to GERD.