Heat the oven to 425 degrees. Line a small rimmed baking sheet with foil. Coat both sides of the chicken breasts with Cajun seasoning.
Heat a large skillet over medium-high heat until hot. Add the oil; heat until hot. Add the chicken and cook for 5 minutes or until well-browned, turning once. Place the chicken on the baking sheet.
Bake for 6 to 8 minutes or until no longer pink in the center.
Meanwhile, melt the butter in the same skillet over low heat. Add the garlic cook for 30 seconds or until fragrant, stirring constantly. Add the shrimp and cook over medium heat 2 to 3 minutes or until shrimp turn pink, stirring frequently. Place the shrimp on a plate.
Increase the heat to medium-high. Add the cream. Bring to a boil and cook until it starts to thicken. Stir in the lemon juice. Remove from the heat. Stir in the sour cream and shrimp.
Spoon over the chicken breasts and sprinkle with green onions. Serve accompanied by prepared red beans and rice or dirty rice if desired.