Shallow well surging

Thanks in advance for any assistance. Please refer to my poor artwork/picture for reference.

My new well has a 30 ft PVC pipe with the last 10 ft being a PVC screen (Yes, it's a PVC screen from a big box store - Two 5 ft sections). The water level was verified at 18 feet using a string and float. When the pump is turned on, it takes 2-3 minutes to prime, then the output reaches a maximum flow of 13 gal/min for about 10 seconds, then slows down to a trickel for a few more seconds, then builds back up to the maximum output. This cycle continues over and over again.
Based on my drawing, is it doing this because the water level is being drawn down below my screen and it's sucking air?? Or is the level just getting too low for my pump to lift due to the atmospheric limitations of jet pumps (I have tried several different pumps with similar results). Is it possible that the available volume of water is just too small in this well?? Should I remove one section of screen to keep the water level up?
Also, when the pump first turns on, the water is very cloudy from extremely fine white sand. I believe it's what we call sugar sand down here in Florida. It eventually clears up.

Thanks

To answer your questions,
Yes, you are drawing the water level down below your screen pipe. It doesn't need to be any more than a foot of screen on the bottom of the pipe.
Second- A jet pump consists of two pipes(one slightly larger than the other) with a foot valve at the bottom with the screen below that. In this configuration, the screen should only be about a foot long and about 2 feet from the bottom of the well. The white sand you see is the pump stirring up the bottom of the well. That should settle down with use.