Add water, salt, and a lemon cut in half to a large pot. Bring the mixture to a boil, then add frozen shrimp. Let cook for a few minutes, about 2-3 minutes, stirring occasionally, until the shrimp are cooked through and pink. Then either remove the shrimp from hot water and rinse with cold water, or add ice to the pot to cool it down and keep the shrimp from continuing to cook.
Let shrimp cool enough to handle, then drain water, if not already done. Peel and devein the shrimp, leaving the tails intact.
For the cocktail sauce, whisk the ingredients together until combined. Store sauce and shrimp in the refrigerator until ready to serve.
Notes
Shrimp and sauce can be made up to 24 hours in advance and refrigerated until serving.