Chop the drained artichokes and arrange them in the bottom of an 8x8-inch casserole dish. Pour the cooked, cleaned and drained shrimp over artichokes. Sauté the mushrooms in 2 tablespoons of butter in a medium skillet. Stir the mushrooms into shrimp/artichoke mixture. Mix the cream, milk, sherry, Worcestershire sauce, salt and pepper in a small bowl; set aside. Melt the remaining butter in a medium skillet. Stir the flour into the melted butter and cook until a light roux forms on medium heat. Turn the heat to low and whisk the milk mixture into roux. Whisk until the sauce thickens. Remove from heat. Stir in the sour cream. Pour the sauce over the shrimp mixture. Cover with cheese and sprinkle with paprika. Bake at 350 degrees for 25 minutes.