No, it was part of what was considered the New World
The contrast between the two sets of organisms, Old World and New World,
His impact still echoes through the centuries. He was the start of the European invasion of the new world. The moment he stepped onto land he brought with him disease, and the old world to the new. The Native Americans would be killed, enslaved, and pushed off ancestral lands by the Europeans. For his part Columbus was a greedy man who wanted riches from his voyages, but he died broke and sick not knowing how he changed the world of Native Americans.
the Old World and the New World Europe and the Americas
The Europeans
Old world is Europe, Asia, Africa, New world is the Americas.
Smallpox originated in "the Old World" (Eurasia and Africa) and was brought to "the New World" (the Americas) by Europeans. So, basically, no. US troops didn't "bring smallpox to Europe" because it was already there.
Disease came with the Europeans. The old world brought diseases to the new world and they had no natural immunity to them.
The disease originated in Africa (old world) and spread to tropical areas of the Americas mostly via the slave trade. It is not currently common to other tropical areas like South and Southeast Asia or the Pacific Islands.
Old World monkeys live in Africa and Asia. When the Americas were discovered, people called the western hemisphere the New World. Europe and the rest of the known lands were called the Old World. That is why monkeys of the Americas are called New World monkeys and those from Africa and Asia are called Old World monkeys.
In the 15th and 16th centuries in particular, Europeans were intent on seeking out a new and faster route to Asian trade-markets than those that already existed. Their searches led to the discovery of the New World of the Americas, which was then explored both for its intrinsic wealth and for the sake of that still undiscovered, and still desired, "Passage to the East."
the Old World and the New World Europe and the Americas
The Old World includes continents Africa, Asia, ans Europe. They were the part of the world the Europeans already knew about before meeting the Americans.