Air Conditioner air is not flowing out of the vents

If you heard the mode doors change while driving, they are not stuck; they were moving.

Without knowing which system you have, your complaint is a common one with vacuum-operated heater controls. If the vacuum hose breaks or comes loose and vacuum to the heater controls is lost, the systems are usually spring-loaded to default to the defrost position. That is done for safety. Your feet might freeze but your windshield will be clear.

Start by looking at the vacuum hose routing diagram under the hood and see if it shows a small hard plastic hose going through the firewall. If it does, check that hose. If you have electric mode door actuators, the problem could be with the controller or an actuator, although a failed actuator will typically leave the door where it is, not move unexpectedly like yours did.