Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Boil noodles in salted water until just tender. Drain and set aside.
Toss chicken with fajita seasoning, salt, and pepper to coat evenly.
Warm olive oil in a large skillet over medium-high heat. Sear chicken until browned and cooked through, 5–7 minutes. Transfer to a plate.
Sauté bell peppers and onion in the same skillet until crisp-tender, about 4 minutes. Stir in garlic for 30 seconds.
Pour in broth. Add cream cheese and sour cream. Stir until melted and creamy. Fold in drained tomatoes.
Return chicken to the skillet and stir in lime juice. Add cooked noodles and toss to coat.
Mix in half the cheddar and half the Monterey Jack. Transfer mixture to the prepared dish. Sprinkle remaining cheese on top.
Bake until hot and bubbling, 15–18 minutes. Broil 1–2 minutes for extra color, if desired.
Rest 5 minutes. Sprinkle with cilantro and serve.