Virtually all of the Columbian Exchange's negative effects were felt by the Indigenous population of the New World. Although the Exchange was mutually beneficial in certain respects, it's fair to say that for the Indigenous Americans, the cons vastly outweighed the pros.
For one thing, the Europeans brought with them all manner of deadly communicable diseases. Indigenous people had never encountered such diseases before and so had not developed any kind of natural defenses against them. The results were catastrophic. Large numbers of Native Americans died of measles, smallpox, influenza, and many other diseases caused by the tiny, invisible microbes that had accompanied European settlers across the Atlantic.
And it wasn't just diseases that came with the Europeans. Rats did too—and lots of them. They hitched a ride aboard European ships, and when the Europeans disembarked, so did they. They helped to spread disease as well as devastating the local flora and fauna.
Sand fleas also came with the European colonists. Sand fleas burrow their way under the skin, where they deposit their eggs. This can cause serious infection, and even death, if the infection isn't treated properly. Many people died as a result of sand flea infection, as the medical knowledge of the day was insufficiently developed.