Also, there are other low risk and 13 high risk hpv virus that the hpv test detects; so YES you could still test positive for hpv. 16 and 18 are the worst; so if you you got the vaccine before becoming sexually active you are protected from these.
The hpv vaccine only protects against low risk hpv 6 and 11 and high risk 16 and 18. There are many others out there. Also, if you were sexually active ,oral, anal, hands touching etc., before you got the vaccine, you could have contracted 6.11,16, or 18.
If by a positive Pap you mean abnormal, then you should be having this investigated.
Write down your questions and don't be embarressed aabout asking ?s It is a Very confusing subject-hpv and pap tests.
YOu are probably fine, BUT get follow ups anytime that your pap is abnormal.