A change in water quality of ...

A change in water quality of a well is due to some immissions into the well or into its ground water aquifer. Faeces (human or non-human) contain considerable amounts of nitrogen, beside the potential input of bacteria. So test for ammonia, nitrite, and nitrate are reasonable.

Concerning toxic inorganic compounds such as arsenic, you have to test for the element. Health related concentrations are too low to be detected by other means. So you need to test arsenic, manganese and so on.

For preliminary assessments you can use rapid assays that give a plausible range of concentration by a colour change of the test kit. Very easy to use even for non educated persons. Of course you need laboratory analysis by more sophisticated methods in case the preliminary test indicates a possible contamination. There are test kits by Merck and Hach and probably from some others.