In a large pot, bring salted water to a boil. Add the linguine and cook according to package instructions until al dente. Drain and set aside.
In a bowl, toss the shrimp with Cajun seasoning until well coated.
In a large skillet over medium-high heat, heat the olive oil. Add the seasoned shrimp and cook for about 2 minutes on each side, or until they turn pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds. Add the cherry tomatoes and cook for another 2-3 minutes, or until soft.
Pour in the heavy cream and bring to a simmer. Stir in the grated Parmesan cheese until melted and smooth, then season with salt and pepper to taste.
Add the cooked pasta and shrimp to the skillet, tossing everything together until well combined and heated through, about 1-2 minutes.