Shallow well probelms

I live in southeastern NC near the coast. I used instructions from Brady well points website to wash down a 2" PVC pipe 35'. I checked the static water level which is at 11'. I then put down three 1 1/4" well points (one coupled to the next) for a continuous wellpoint of 12' with 23' of 1 1/4" pipe on top of the continuous well point. I then pulled the 2" casing out of the ground. I piped the 1 1/4" pvc pipe to my 1 HP Goulds shallow well pump. I have a check valve between the top of the "well" and my pump. I didn't get more than ~ 1 GPM so I added three more wells tied together in an H pattern with each well an equal distance from the middle of the H pattern. From the middle of the H pattern I have a tee which goes to the pump. Each well has its own check valve. I have a vacuum guage that shows greater than 25 when I am running the pump and water is flowing. Even with four 1 1/4"wells ( one at 35', two at 31' and one at 27.5') the pump will produce a strong stream of water for 15 seconds and then die where no water flows for 8-10 seconds before pumping a strong flow of water for another 15 seconds. The pump will build up pressure and then turn off if I shut off the spigot I have on the outlet side of the pump. I have a small pressure tank installed. What am I doing wrong? Any help will be greatly appreciated.

Sounds like you need to drill a real well.