Thank you so much, that is so reassuring. :) And I'll definitely look into Gardasil 9!!
This isn't a surprise at all. Gardasil (the original version that you had) prevents 4 of over 100 HPV types, incuding only 2 of about 20 high risk types. (It also prevents infection with the two types that cause almost all genital warts.) Those two are very important, since they account for about two thirds of all high risk HPV infections. But many women still catch HPV, including high risk strains, after Gardasil. That doesn't mean the vaccine wasn't effective or that it didn't benefit you. It did, by preventing 70% of HPV infections that might lead to cancer if not treated, as well as genital warts.
A new version of Gardasil -- called Gardasil 9, because it covers (guess what?) 9 HPV types, the same 4 as before, plus 5 more high risk types. Obviously it won't prevent infection with any HPV infections you already have had, but still is something you should have. Discuss it with your doctor.
As for your two doctors' opinions, I suggest you talk it out with the second one. She is exactly right, that any HPV you have will probably be cleared by your immune system. You may need follow-up testing and paps, but the large majority of women in your situation never have any serious health problem from HPV.
And HPV has absolutely no effect on ability to conceive and bear healthy kids. This also is something for you to discuss with the second doctor -- along with considering Gardasil 9.
Good luck. Don't be worried!