Shrimp tend to be pretty sensitive to water quality (i.e. nitrites and ammonia), so that would indicate that your tank has indeed not cycled properly. Fish can often survive poor quality water, but they will be suffering and will have reduced lifespans and be more prone to disease.
I would start dechlorinating your water religiously. Also, if you can get hold of some filter media from an established tank, add that to your own filter media. Still might take some time though.
I am not an expert on all this George, others may have an opinion, but as I said you should probably re-read the basics to make sure you aren't missing any other key elements to keeping an aquarium.