Bring a large pot of salted water to a boil. Cook linguine according to package directions until al dente. Reserve 1/4 cup pasta water, then drain.
While pasta cooks, pat shrimp dry and season with salt, pepper, and red pepper flakes. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Cook shrimp 2-3 minutes per side until pink and opaque and they reach an internal temperature of 145°F (63°C). Transfer to a plate.
Reduce heat to medium, add remaining 1 tablespoon oil and garlic. Sauté 30 seconds until fragrant. Pour in heavy cream, lemon zest, and lemon juice. Simmer 2 minutes, then whisk in Parmesan until melted and smooth. Stir in reserved pasta water gradually until sauce coats a spoon.
Add drained pasta to the skillet, tossing to coat. Return shrimp and any juices to the pan, gently folding to combine. Cook 1 minute more to reheat. Serve immediately with parsley and lemon wedges.