In addition to runoff, ...

In addition to runoff, rivers receive groundwater from adjacent soil, which moves into the river channel. This is called "base flow".  A well that is located close to a river may reverse this flow and draw water from the river. Thus, it is likely that at least some of the water that is flowing into your well comes from the river, particularly in cases of sandy soil. Lab tests are not the best way to determine this, but there are other ways of estimating the effect of the nearby river on a well. Look up a groundwater hydrology text or the USGS website.