Fresh shrimp only last a day or two in the fridge before becoming unsafe to eat. Freezing shrimp is easy, and doing it properly minimizes any effect on its flavor and texture.
Chill the shrimp in the refrigerator before moving them to the freezer in containers or freezer-safe storage bags, and seal them with an inch of clearance from the top.
You can leave the shells on whole shrimp or peel and devein them, and be sure to remove the heads. Leaving the shells on helps to maintain their flavor and texture.
To freeze cooked fresh shrimp, remove the shells. Tails can optionally be left on, depending on how you intend to use your shrimp in the future, such as for cocktail shrimp.
Thoroughly wash and dry your shrimp if you're freezing them raw, and label the bags with a "frozen on" date. Frozen shrimp will last in the freezer for about three to six months.