I just read an articlette on this yesterday. They said that Americans drove on the left, just like the British, which developed so that people going past each other faced their weapons hands to each other. Later, when driving carriages became a thing, the driver stayed on the right to have full freedom of his whip hand (presumed to be the right) and could see if he were going to foul wheels with a vehicle going the other direction.

In America, they developed long-distance freight into the frontier and back, using the massive Conestoga wagon. This had no driver's seat in front. It was driven postilion style with the driver on the near/left wheeler, so his whip could reach any horse without the height advantage. So Conestogas drove on the right, and so did anyone who might meet one, and the habit spread from the country into the cities.

In the cities, in horse drawn days, there were no traffic lanes. You stuck yourself in where you could, so the shift wasn't that hard.

Edit

The Conestoga developed in Pennsylvania in the early 1700s.