Can you freeze shrimp?
Yes, you can freeze shrimp
Best quality within 6 to 18 months, depending on the kind.

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.
fresh (shrimp, crayfish)
Up to 6 to 18 months
purchased frozen
Up to 12 to 18 months
Keep frozen. For safety, cook as directed.
What the freezer time means
Freezer times from USDA FoodKeeper are about quality, not safety. Food kept frozen at 0 F (-18 C) stays safe indefinitely; what changes over the months is texture, moisture and flavour. Wrap shrimp tightly, press out air, and label the pack with the date so the window above is easy to track.
Thaw in the fridge, not on the counter. Anything that thawed in the fridge can be refrozen, with some further loss of quality; anything left at room temperature for more than 2 hours should not go back in.
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.
Can you freeze other seafood: shellfish?
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.