Rather than VOCs, you might want a hydrocarbon scan. You want to keep your animals away from the water. The source could be a pipeline, diesel fuel, home heating oil and it may be from a 'spill' from many years ago.
Carbon is used to remove it but, you may find that the carbon becomes hazardous waste and can be expensive to get rid of. It takes someone that knows what they are doing to successfully treat it with special set up of the filters. You could buy the equipment online and install it yourself but regardless where you were to buy it, you will have to follow instructions specifically to maintain it properly.
Some will probably suggest a new well, there is no guarantee that a new well wouldn't have the same problem now or later. Finding the source if possible is important.