Cook macaroni in a large pot of water with the tablespoon salt until just tender. Reserve 1/2 cup pasta water, then drain.
While the pasta cooks, heat oil in a large skillet over medium-high heat. Season chicken with the remaining salt and pepper and cook for 7 to 9 minutes, turning, until browned and 165°F in the centers.
Lower the heat and add milk and cream cheese. Stir for 3 to 4 minutes until the cream cheese melts into a smooth sauce.
Stir in hot sauce, then remove from the heat. Fold in Monterey Jack and cheddar until melted.
Add the pasta and toss, using reserved pasta water 1 tablespoon at a time if needed to loosen the sauce. Serve hot.