After I buy any fish I generally rinse it well in cold water and place it in an air tight container. I then place the container in the bottom of the refrigerator on top of an ice pack (the type that you would use in a cooler). The ice pack will stay frozen for about 36 hours in the fridge and keep the fish cold without freezing it.
I often buy frozen shrimp but if I am going to use it quickly I will buy thawed shrimp at the market. I then shell it and store it in a tightly sealed container on ice packs. I don’t, however, devein shrimp until I am ready to cook it.