Overheating and cooling system problems

1997 Pontiac Grand Am SE 2.4Liter V6.

I've been struggling with an overheating problem with my car for a few years. Everytime I take it in the mechanic "pinpoints and repairs" the leak, only to have it overheat, presumably from lack of water, a few days later.

My latest repair involved a new radiator, thermostat, heater core (the previous one had. Well. Exploded.) And any hosing that looked questionable. Didn't work.

After my latest boiling over, I got air in my system. How can I tell? Well. Everytime the car changes motion (stop, go, turn, etc) I can literally hear water sloshing around. For instance, a right turn will give off the sound of a water trickling from a left to right, resonating from just behind my dashboard.

Also, if the car starts to get hot, my heater will only blow cold air, if it suddenly goes to hot air (as it sometimes does.) The engine temp immediately drops.

I had the radiator flushed yesterday hoping to get the air out before the whole thing becomes vapor locked (as happened before all the repairs) but I still hear the "sloshing" and sure enough, my car boiled over on the way home.

Is there a chance that a part in my latest set of repairs is faulty, or do I need to just keep searching for this phantom water leak?

For the short term, how do I get the air out of my cooling system? The car was easy enough to maintain water-level-wise before the air got in, only needing a bit of water every 3 days or so.

Thanks in advance.