It sounds like the HVAC control head has a leak or has failed.
The motor which blows air through the vents.
Any of the following can cause this......... 1. Bad a/c - heater controller.. 2. Bad a/c - heater controller inside door operation.. 3. Bad, broken or cracked vacuum line/lines..
There are heater doors on the heat blower box that direct the path of the heat. Apparently the heater door to the floor vents is stuck closed.
Bad heater core.
The heater core has failed.
Could be that your heater core is leaking May also have a plugged evaporator hole.
Leak in heater core. Replace core.
Leaking heater core
Most of the time it is caused by a hole in the heater core, do you smell a sweet smell? The sweet smell would be the antifreeze.
SOUNDS LIKE THE INTAKE GASKET BLEW, OR THE HEATER CORE FAILED.. EITHER WAY, THIS IS A COSTLY REPAIR.
Warm(er) air rises - if vents were high up there would be little circulation without fans.
The heater core is leaking coolant.