I did some research on how to determine the output potential of a well, and basically, there is no easy DIY way using a single speed pump. One would need to use a variable speed pump and measure the flow rate and drawdown. Based on this info, there are some basic hydrology equations that can then be employed to estimate well production. But like I said, this approach is impractical with a single speed motor installed for production. Though you could disconnect the pump line from the pressure tank and pump the well while measuring the depth to ground water. If the water level doesn’t drop or stabilizes quickly, and then stays constant after several hours of production, then you would probably be fine upgrading to a ¾ or 1 hp motor.
Your best approach would be to call local well drillers and ask them if they installed any wells in your area, especially in the last couple of years. They would have had to do some basic well test and they will know what size of pumps people have. In short, this is the best DIY step to determine your wells potential.
Also, toy4xfun mentioned that they tasted chlorine in their water after the neighbor disinfected their well. This would imply that the neighbor’s well is upgradient and their production may impact the yield (over lapping cones of depression). Furthermore, if you know when they dumped the chlorine and when you first started to taste it, one could do a rough order of magnitude estimate on the hydraulic conductivity of the aquifer, which would be useful information.
In typing this, the other thought that occurred to me, is what kind of aquifer is the well completed in. If it is in limestone/dolomite/marble, then well production may not be an issue at all.