I went to the doctor yesterday and they said the white stuff on my throat I was seeing was actually scar tissue from having my tonsils removed years ago. I plan on getting a Pap smear feb 10 and I will ask about the shot then.
Go to an ENT doc or to an oral surgeon to get any bump removed and biopsied for HPV. No matter what happens, get the vaccine so that you are not infected by any strains you don't already have. GYNs are for genital issues, not throat issues. Eventually, get a Pap done to know about your genital health.