As a child of the '60s, I have a very soft spot in my heart for old-fashioned shrimp cocktail... It was THE hors d'oeuvre at cocktail parties and THE starter for fancy restaurant meals... Try it again, and you'll be amazed at how good the real thing is...
Buy a bag of frozen shrimp (yes, I said "frozen..." unless you live IN the water, you've probably never had truly fresh shrimp, and that's OK because shrimp spoil so fast that freezing at sea is a great idea)...
Thaw them, shell them, and devein them if needed; leave the tails on for great "handles..." and
DO NOT OVERCOOK THEM!
Two easy ways: Put them in a saucepan with water, white wine, salt, peppercorns, and red pepper flakes. Slowly bring to a simmer and, as soon as you see the shrimp just start to turn pink, TURN THE HEAT OFF. Let them finish cooking and then cool in the broth...
An even easier method is to toss the shrimp with olive oil, salt and pepper, and then roast them in a 375°/400° oven for about 9 minutes...
And cocktail sauce is simple to make: mix some ketchup, prepared horseradish (but fresh grated is even better!!), and a little lemon juice. Of course you can add some hot sauce if you want!

Shrimp Cocktail