In a large pot of boiling salted water, cook the fettuccine according to package instructions until al dente. Drain and set aside, reserving a cup of pasta water.
In a bowl, toss the shrimp with Cajun seasoning until evenly coated.
In a large skillet, heat olive oil over medium-high heat. Add the seasoned shrimp and sauté for 2-3 minutes on each side until they turn pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant. Pour in the heavy cream and bring to a gentle simmer.
Stir in the grated Parmesan cheese until melted and smooth. Add in the sun-dried tomatoes and mix well. If the sauce is too thick, add reserved pasta water gradually until the desired consistency is reached.
Add the cooked fettuccine and sautéed shrimp to the sauce. Toss everything together until the pasta is well coated. Season with salt and pepper to taste.
Once everything is combined and heated through, remove from heat. Sprinkle fresh parsley on top and serve immediately with lemon wedges on the side for a refreshing finish.