Have you tried filling the point from a hose? There is supposed to be an equivalence between the flow of water you can pour into a point and the flow of water you can draw from it.
Also, there is the matter of "developing" the point, to get fine particles away from clogging the screening. I had points where the soil was not even close to ideal sandy conditions, and I would occasionally have to spend time clearing the screen, by forcing water in, then pumping it out, and repeating the process for as long as it took for particles to stop accumulating in the 100-mesh strainer I had installed in the pump output.
A water table at the 20-foot mark may limit what you can draw, using a shallow-well jet pump. Invest in a deep-well convertible jet pump, with a packer ejector assembly in the well, and you get past the depth limitations of the shallow-well jet pumps.
By the way, what were you using to drive the well point?