In a large mixing bowl, combine the diced tomatoes, red onion, cilantro, and jalapeño. Squeeze the juice of one lime over the mixture, add a pinch of salt, and toss to combine. Stir in the cocktail sauce. Cover and refrigerate while preparing the shrimp.
For Raw Shrimp: Place shrimp in a colander, rinse with cold water, and drain well. Remove tails if necessary. Bring a large pot of water to a boil, add about one tablespoon of salt, and cook the shrimp for about 2 minutes, or until the shrimp turns white with pink accents. Drain the hot water and cool the shrimp by covering them with cold water. Drain and transfer shrimp to a cutting board.
Cut each shrimp into two or three pieces, reserving some whole shrimp for garnish. Add the rest of the shrimp to the cocktail sauce mixture and stir to combine.
Just before serving, pit and chop the avocados, squeezing the juice from the remaining lime over the avocado to keep it fresh.
To Serve:
In a Bowl: Garnish the top of the shrimp cocktail with avocado chunks, reserved shrimp, and a sprinkle of cilantro. Serve with tortilla chips or saltine crackers.
For Individual Servings: In serving glasses, layer a spoonful of the shrimp cocktail mixture, followed by a layer of avocado. Fill each glass to the top with more shrimp cocktail, and garnish with additional avocado, cilantro, and reserved shrimp.
Make Ahead Instructions:
Prepare the pico de gallo mixture and cocktail sauce a few hours in advance, cover, and refrigerate until ready to serve. Add shrimp and avocado just before serving for maximum freshness.