silt in lake fed well

I have a lake fed well. It's a culvert sunk into the ground about 20 ft from the lake then water is pumped up to the cabin. The water enters through the bottom of the culvert / well and up until now was filtered by the sandy bottom. Usually I have about 4 ft of water of fairly clean water for dishes and showers. I accidently ran the well dry and here's where the problems started. It appears that silt has entered the system and my water is now very dirt and cloudy. The particles are very fine and even after sitting for almost 2 weeks it did not settle. I immersed a pump and pulled out all but about 2 feet of the water. I was able to reach inside with a paddle attached to a pvc pipe and try to stir up the muck that way (with the idea that the silt density will eventually decrease) and we'll be left with clean water again. New water entered the well (I cant see it entering but it did rise) but it didn't appear much cleaner than before. Another option is getting into the well (culvert) and manually removing a foot or 2 of the bottom layer with a shovel and pails. This may or may not help. Someone mentioned we may have opened up a "new channel" coming into the well and we're getting straight lake water. (I don't really understand this because we were always getting lake water, maybe he meant straight unfiltered water). Thoughts anyone? Open to suggestions. I'm hoping to avoid having to dig a whole new well - which is really not in the budget.

I am by no means an expert on wells, so take this with a grain of salt. But I think for some reason or another, you are getting unfiltered lake water. You could de-cap your well if it is a hand dug well, and dig it deeper, then plug the source of the unfiltered water and use dry stacked stone and small gravel to act as a buffer between the saturated earth and the well proper.