1992 Cadillac Deville Blowing hot and cool air at the same

F48 would probably disable the A/C compressor, and therefore not be affecting the air. Was the system low on coolant prior, or did this happen after draining it. The 4.X series of engines do capture air when the system is drained, usually up behind the thermostat since it sits highest of all in the cooling system. It sounds like you are getting warm water flowing through the core, and the reason the drivers side is cool, is because it is furthest away from the core. Are the hoses hot, at the core inlet/outlet, as well as the radiator hoses? If everything is hot, and you are sure coolant is flowing, would suspect a clogged heater core. Especially, if the compressor is not coming on.

What lead you to that conclusion? Are both heater hoses at the core cool indicating no/little flow through it? About the only way I know to flush it is to connect a water hose to one end, and open the other end to drain. Reverse if necessary. You can also check the flow at this point. The way the core sits in the box, the lines are at the upper end, and it stands vertical, so any debris will be stuck at the lowest point.