Rinse and drain the shrimp. Press between paper towels to remove any excess moisture. Stir together the shrimp, pico de gallo, salsa, and lime juice in a small bowl. Cover and allow to marinate for 10 minutes.

Place an equal amount of cheese, avocado, and shrimp mixture on half of each tortilla. Fold over to enclose the filling. Place on grill over low heat and cook for 3 to 5 minutes, or until lightly browned. Carefully turn and grill the other side. Serve warm with sour cream.