"Putting up" shrimp, or other seafood, is often used here in Charleston for freezing the shrimp. Either by just washing and packing in ziplocks or the milk carton method, and covering w/water, or by heading them first, then packing for freezing. Some folks also add about a tsp. of salt to the water.
I've made pickled shrimp, but I'm not sure you could put this up for long term storage with just a hot water bath - I think you'd need a pressure canner. Just did a quick google, and couldn't find anything specific. I'm just not sure if the vinegar used in the pickling process would be enough acid to go ahead with the hot-water canning method.
Paula's recipe mentioned above is wonderful, I can vouch for it; but I think she only says the pickled shrimp will store for a few days in the fridge, not as a 'long term' pantry item.