My faucets spurt air when I use them. I have a well and wonder if it is a problem with the air volume control in the pump or is it with the softener, which was installed a few months ago. Could it be something else?

I vote for the air volume control. How long has this been going on. Did it occur before the installation of the water softener. Water softener should have a bypass valve. Try bypassing water softener to see if there is any difference.