Bring a large pot of salted water to a boil. Cook the linguine according to the package directions. Drain water. Set pasta off to the side.
Heat a saute pan over medium heat. (I would just use a frying pan as I don't have a saute pan.) Add the olive oil and shrimp. Cook, stirring until the shrimp are mostly pink with some grey remaining.
Add the garlic and continue to cook until aromatic and starting to brown. Stir in the pepper flakes, tarragon, artichoke hearts, and cherry tomatoes. Continue to cook to heat through. Toss with linguine.
Taste and adjust the seasoning with salt and pepper. Drizzle with lemon juice. Divide between 4 bowls. Sprinkle with Parmigiano.