City tap water in Europe and North America is regularly tested for common parameters and yearly, more or less, for most other constituents(pollutants, minerals, chemicals etc.) It is very very unlikely you got sick from the tap water. If you want to test your own water, find an "environmental laboratory". Communicate with them, they will help you decide which range of tests. They will also provide you with the appropriate sample bottles. (There are organic and inorganic parameters with different protocols for sampling.) It won't be cheap however. Especially one time testing. You can spend anywhere from ($CAD) 50-150 for inorganic tests (arsenic, lead, etc.) And 150 - 500+ for organic tests ( DDT, PCB, etc etc.) Cheap and easy - but all cities do it all the time, is hardness, pH, etc. If you are suddenly sick it is likely organic, and most likely biological (bacteria, virus.) Also most likely from food. But, it is fun to test your water, and interesting. (Same with the soil around you.) The world around us complex and the interweaving of systems is fascinating; as is our infrastructure to allow city living. (Source for my diatribe: 20+years Environmental Engineer)