Welcome to our Forum and thanks for your questions.  I'll be glad to comment.  Congratulations on having received the vaccine which will certainly reduce your risk for acquisition of future HPV infection.

There are well over 100 different types of HPV.  Over 80% of unvaccinated, sexually active persons will acquire one or more HPV infections at some point with the first infection typically occurring within a year or two of becoming sexually active.  The HPV vaccine, depending on which one you got provides over 95% protection from the two HPV types which cause most visible genital warts and either the two or seven HPV  types which most commonly cause most pre-cancerous PAP smear changes.  It is not at all uncommon for a woman to have acquired an HPV type which was not covered by the vaccine but fortunately, the risk of such infections proceeding to pre-cancerous lesions is even lower than for the vaccine types.   You are unlikely to ever know when you got the HPV that showed up in your PAP smear.  In some instances, HPV infections which have been suppressed by the immune system transiently reactivate and are detected on PAP smears.  This is not a cause for concern and does not mean that your positive test is a threat to your health.  Given what you describe, the way forward is to simply continue to have your regularly scheduled reproductive health checks/PAP smears.

The warts you noticed recently may or may not have been missed with prior exams so as noted above, you are unlikely to know where or when your infection occurred.

As for partner notification, we do not feel strongly that persons with HPV infection need to disclose the fact of their diagnosis to prior partners, nor do they need to take special precautions to prevent future transmission.  As noted above, whether they know it or not, most sexually active persons, including your current partner have already acquired HPV.   

I hope this information is helpful.  Questions about HPV, disclosure, and the significance of positive tests are among the mst common questions we receive on the Forum.  I would encourage you to look at other threads on the site- we keep them available so others can see what the information we provide.

If any part of this is unclear.  Please don't hesitate to use your up to 2 follow-ups for clarification.  EWH