Blowing cold air when heater is on, needle is over heating, antifreeze looks to be sprayed all over engine?

1996 Ford Crown Victoria LX 4.6

Just changed the thermostat today so that wasn't the problem.

Although when changing the thermostat, there was a crap ton of antifreeze in the thermostat housing.

Both hoses going in and out of heater core were warm/hot.

Your symptoms are dead on for a defective thermostat so its odd that replacement didn't fix the issue. I would check the water pump to see if its working properly. When you start the car, the upper radiator hose should be firm.Let the vehicle warm up to operating temp then squeeze the upper hose and release, but keep your hand on the hose to feel for a pressure surge. If a pressure surge is not felt, the water pump might not be pumping sufficiently. This will cause overheating because coolant is never circulated fast enough. If the upper hose continues to be firm when the vehicle reaches operating temp, the thermostat is sticking shut or you've got it installed backwards.Spring side goes towards the intake. If the vehicle is at operating temp and the thermostat is open, you can remove the radiator cap after you release pressure, coolant should be flowing freely out of the tubes inside the radiator. If not, the radiator may be clogged or the water pump isn't working correctly. Check heater core 4 clogs