As a restaurant owner and Chef I am sometimes faced with the same situation. I have an abundance of raw Shrimp, It's early in the week and I need it to keep until the weekend. The best way I have found is to keep it as air tight as possible and always date the package. One method you can use is to add a teaspoon of lemon juice to a 1/4 cup of Olive Oil and coat the shrimp before storage. This method will keep it longer however there are some things to consider. The lemon juice will raise the acidity level thus buying you more time. On the other hand, one downfall of that is that the acids in the lemon juice will slowly cook the shrimp which is why I suggest using a small amount. You can even go with just the Olive oil. It will act as a great marinade as well. But normally, if kept as air tight as possible, without using any marinade, Shrimp should last up to 7 days.
Remember to always use the best culinary tool God gave you. Your Nose. If you're using a Mexican Shrimp (common) they are gray in color...they will tend to turn a slight pink/orange when they are bad (a similar color to cooked shrimp). But if they are bad you will most certainly know. When it comes to seafood...bad is bad and good is good. It's pretty cut and dry.