A Reverse-Osmosis filter system will remove it for drinking water, but does not have the capacity for the whole house. I am not certain, but a whole house water softener system may remove sodium. Call your "Culligan Man". It should be resolvable.
Have it tested further and check into filteration and/or conditioning systems which address the bad things in your water. You can go to your local analytical laboratory and get a kit for testing the water. The well driller will only be able to suggest relocating the well or drilling it deeper, with no guarantee of results.
They sure would have saved a lot of problems by getting a 50.00 test done.