Noise

You have actuators that move the blend, recirc, and mode doors. These are the little plastic flaps that direct air around. When bad the actuator can make a clicking noise. If the doors themselves are stuck or popped out of their swivel hole they can make noises as well. You also have a blower motor in the dash, but your description doesn't sound like the sort of noise it would make when bad. You will also have various relays and modules that can make noises, typically ticking noises, when they go bad. I would look up a diagram of your car's heater and AC ducts, and check all the actuators.