There's a fairly universally accepted theory that Syphilis was from the Americas, and a few other diseases (like a close relative, Pinta) were present, although most of those were chronic and episodic or opportunistic like HPV infections, versus the acute and epidemic diseases that come from living in comparative filth and close contact with livestock. Of these, the only one we have records of actually breaking out in Europe is Syphilis, which first became readily apparent with the 1494-95 Epidemic in Naples during a French Invasion of the area, and then just followed military movements, since it is an STI and was generally carried around by soldiers and travelers. Of course, Syphilis went on to be a massive and constant public health crisis across the entire planet (but especially Europe.) Some HPV strains might have also made the jump, but I don't think anyone has been able to trace HPV strain movement across the Atlantic to that specifically.

It's also about the only thing we could expect to develop in a situation like the americas and be capable of flowing into Europe from first contact, since STIs are chronic lifelong conditions that kill slowly and incidentally, and aren't as reliant on population density to maintain themselves. Therefore they can spread further temporally and geographically than epidemic diseases that require massive interconnected populations to sustain themselves in an endemic state. European epidemics that came to the americas OTOH were comparatively fast acting epidemic diseases that were IIRC universally derived from zoonotic diseases, and were absolutely devastating in ways they hadn't been in Eurasia since the neolithic or they evolved (and were capable of th absolute devastation seen in the Americas when unlashed in prehistory, as they decimated communities incapable of sustaining them as endemic diseases.) Meanwhile HPV and at the very least some of the Treponema pallidum diseases (the bacteria that causes Yaws, Bejel and Syphilis) are incredibly ancient legacies from early humans that almost certainly came with the initial peopling of the Americas, and then Syphilis evolved from Yaws some time in prehistory.

Sources:

1491: New Revelations of the Americas Before Columbus - Charles C. Mann (Knopf, 2005 edition)

Against the Grain: a Deep History of the Earliest States - James C. Scott (Yale University Press, 2017)

"Health conditions before Columbus: paleopathology of native North Americans" - Martin and Goodman https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1071659/

"The Origin of Syphilis" https://sexinfo.soc.ucsb.edu/article/origin-syphilis