What would cause air to be pushed into pipes from a well tank?
It's possible it's the pressure tank. To check the pre-charge, turn the pump off, and then open a faucet to let all the water out. Check the pressure in the tank using a tire pressure gauge (there is a valve on the top). This should be 2-10 PSI below the "start" pressure of the pump: eg, if your pump comes on at 40psi (on at 40/off at 60 is the most common setup), the pressure tank pre-charge should be 30 to 38psi. If it's lower, fill it (and keep your faucet open). If the bladder is broken, you won't be able to fill it and there will be air coming out of the open faucet.

It's also possible something is wrong with the check valve and air is getting in the line from the well to the house. To check this, turn the water off to your house (usually there is a valve somewhere after the pressure tank) -- it's essential to isolate the pressure tank from the rest of your house to do this test. Run the pump until the pressure tank is full and it turns off, and then watch the pressure gauge. If it's slowly going down, you are losing water somewhere either due to a break in the pipe, or a broken check valve.