if u can run a garden hose full blast into the well and water never comes up, the well will produce water. "if it'll take water, it'll make water".
if the casing is in fact 2".. I would recommend that u quit pulling directly off the casing and install a 1" pvc drop pipe no more than 30' with a foot valve on the bottom.. use a doubletap fitting or 2"-1" well seal and plumb into the pump. then prime and run it off a while. 13' isn't a bad water level so long as the well produces. most shallow jet pumps will pull water from as deep as 25'. good luck.