That's unlikely. Part of the reason for the one way transmission of disease is simply the fact that Europeans were the ones making the crossings. Plenty of europeans got sick in the new world, but they either died in the new world or died on the ships during the long return journey. For a disease to cross the ocean, a carrier who is adapted to the disease must make the crossing. A few natives did go to Europe, but they were likely to die en route while surrounded by Europeans in rather unsanitary conditions.

Further, the europeans making these journeys were typically young and fit individuals who, again, could survive long voyages at sea and the difficulties of setting up new colonies. The elderly and infirm stayed in Europe. Thus the europeans were far less likely to suffer an outbreak of disease simply by virtue of having fewer human incubators. For the natives, however, there was nothing to prevent their most vulnerable from being exposed, nor any way to stop isolated cases from blowing up into large scale pandemics.

The only ways for a counter plague to get to Europe would be for either large numbers of natives to successfully cross the atlantic, which is unlikely when their population is simultaneously being decimated by disease, or for the Europeans to pick up a disease that took a long time to cause serious problems and thus could survive the return journey, which may have been the case for Syphillis. Either way, an "America Pox" is highly unlikely.

Not quite a plague, but syphilis likely came from Native Americans.