Well many of the diseases we had are relatively recent on an evolutionary timeline, coming from our domestication of animals. Concentrated populations of humans living in cities is also relatively new. Diseases wouldn't spread as easily before that.
Many of the diseases have diagnosis and classifications only in the recent times. Before that it was just that a person would fall ill, and then die.
Now we have the most detailed and granular classification, hence we feel the diseases are appearing now.
But I think most diseases existed back then too.
Cholera and HIV also evolved recently and thrive because of denser populations.
The statistics also show infectious diseases declining a lot over the last hundred years so I you're theory can't be correct.
The reason was that European peoples had exposure to some kinds of disease that peoples in the Americas did not. Civilizations in the Americas had domesticated animals for quite some time, just different kinds of animals.
The Europeans had much more hard-core diseases because of a mix of factors (including animal domestication), but the chief one was population density.
European diseases evolved in tandem with the people themselves -- each time something swept through the population and crippled/scarred/killed large numbers of the people, the folks with some level of natural immunity would be favored. The diseases would evolve (at a rapid pace, due to reproducing at enormous scale...), as would the people (very painfully).
People in the Americas were mostly more widely spread out. A nasty variant on a disease that wipes out a village and stops there goes extinct.
There were some cities, trading between areas, etc., but not on a European scale.
(Source: "Guns, Germs and Steel", which went into this all in fascinating detail... though admittedly I read it years ago now).
The other factor that hasn't been mentioned is that a disease can be deadlier when the population density is higher. The disease can find another host to infect before the original dies and still stay active. Whereas in a situation with spread apart populations the deadlier variant would die out once the small local population was killed.
The European diseases carried this much deadlier profile and thus were more effective in killing native americans than native american diseases were in killing americans.
Basically, Europeans had domesticated animals on a much larger scale than a few llamas a few places on the continent. It was deeply integral to the old-world way of life in a way that Native American culture didn't even come close.