In a large pot, combine the shrimp, 4 cups cold water, salt, thyme, peppercorns, bay leaves and celery seeds. Cook this mixture over medium-high heat, stirring occasionally, until the water registers 170 degrees and the shrimp are just barely beginning to turn pink, about 5-7 minutes.
Remove the pot from the heat and add 1/4 cup of fresh lemon juice, along with all of the lemon peels. Cover the pot and let the shrimp mixture rest until the shrimp are completely pink and firm, about 5-7 minutes. While the shrimp finishes cooking, set aside 8 cups of ice next to the pot. When the shrimp are bright pink, stir the ice into the pot and let the shrimp cool completely, about 5 minutes. Remove the cool shrimp from the pot and refrigerate until ready to serve.
Whisk together the cocktail sauce ingredients and chill in the refrigerator until ready to serve. Enjoy!