How to store shrimp
Best place: the fridge. USDA gives shrimp a fridge time (1 to 3 days, from the package date) and no pantry time, so it belongs in the fridge as soon as you get home. The freezer gives 6 to 18 months.

Where these times come from. USDA FoodKeeper has no entry named "shrimp". The 2 kinds on this page are the USDA entries that cover shrimp, copied without change from Shrimp, crayfish and Shrimp, shellfish. Each row in the table is one USDA entry; pick the one that matches what you have.
No guideline
1 to 3 days
from the package date
6 to 18 months
best quality within
USDA notes for shrimp
- purchased frozen: Recommendation is for storage after cooking.
- purchased frozen: Keep frozen. For safety, cook as directed.
How to tell shrimp has gone bad
- Raw shrimp, scallop and lobster flesh should be clear with a pearl-like colour and little or no odour.
- A sour, rancid, fishy or ammonia smell in raw or cooked shellfish means do not eat it. These odours get stronger after cooking.
- Live clams, oysters and mussels should have closed shells, or shells that close when tapped. Throw out any with cracked or broken shells, and any that stay shut after cooking.
- Use fresh shellfish within 2 days of buying, kept at 40 F (4 C) or below, or freeze it. Cooked shrimp and shellfish keep 3 to 4 days in the fridge.
Sources: Selecting and Serving Fresh and Frozen Seafood Safely (FDA). The times on this page are quality guidelines, not safety limits; food that shows these signs goes out regardless of the date.
Storage habits that make the difference
Store live shellfish in a breathable container, like a bowl covered with a damp cloth, never sealed in plastic or submerged in water. Keep them cold, near 32 to 40 F (0 to 4 C), and cook the same day if possible. Refrigerate cooked shellfish and shrimp promptly and use within a couple of days.
How to store other seafood: shellfish
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.