The problem is bacteria build up in the air ducts. The heater core and air conditioning evaporator are housed in one unit behind the dash. There is a drain tube that allows moisture to run out of the bottom of the heater box and drip out under the car near the firewall ensure this hose is not blocked. I wonder too if a mouse or rodent could have built a nest in the heater ducts. We see this often during the winter. We open the engine air filter housing or take down the cabin air filter and find the filter clogged with debris.
The air coming into the car comes from around the bottom of the windscreen ensure this area is clear of leaves and debris.
Try spraying antibacterial spray in to the air ducts let it sit and then leave the fan on high for a few minutes to kill bacteria.