Heat 2 tablespoons of olive oil in a large saucepan over medium heat. Stir in the garlic; cook 2 minutes. Add the tomatoes, and wine. Bring to a simmer and cook 30 minutes, stirring frequently. Once the tomatoes have simmered into a sauce, stir in the butter and season with salt and pepper.

Fill a large pot with lightly-salted water; bring to a rolling boil; stir in the linguine and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through but is still firm to the bite, about 11 minutes. Drain well in a colander set in the sink.

Season the shrimp with the Cajun seasoning, salt, and pepper. Heat the remaining 2 tablespoons of olive oil in a large skillet over medium-high heat. Stir in the shrimp and cook until pink on the outside and no longer translucent in the center, about 5 minutes. Stir the shrimp into the pasta sauce, then stir the sauce into the linguine to serve.