Bring a large pot of salted water to a boil. Cook linguine pasta according to package instructions until al dente. Drain and set aside.
In a medium bowl, toss the shrimp with Cajun seasoning until evenly coated.
Heat olive oil in a large skillet over medium-high heat. Add shrimp and cook for 2-3 minutes per side until pink and opaque. Remove shrimp from skillet and set aside.
Reduce heat to medium and add butter to the same skillet. Once melted, add minced garlic and sauté for 1 minute until fragrant.
Pour in chicken broth and bring to a simmer. Let it reduce slightly for about 2 minutes.
Stir in heavy cream, Parmesan cheese, lemon juice, and crushed red pepper flakes. Cook for 3-4 minutes, stirring frequently, until the sauce thickens.
Season the sauce with salt and freshly ground black pepper to taste.
Return the cooked shrimp to the skillet and toss to coat in the creamy sauce. Cook for an additional 1-2 minutes to heat through.
Add the cooked linguine to the skillet and toss everything together until the pasta is well coated with the sauce.
Sprinkle chopped fresh parsley over the top and serve immediately.